discrete mathematics - Calculate number of small cubes making up large cube given number in outermost layer - Mathematics Stack Exchange Calculate number of small cubes making up large cube given number in outermost layer up vote 5 down vote favorite 3 I have a large cube made up of many smaller cubes. Each face of the cube is identical, and all of the smaller cubes are identical. I need to calculate the number of small cubes that make up the large cube. Just to make it clear, the cube is solid (made up of little cubes all the way through). The only value I have to work this out from is the number of small cubes that make up the outermost layer. This number is $100,614,152$. What is the simplest way to calculate the total number of small cubes making up the large cube? Is this homework? – Jonathan Christensen Dec 6 '12 at 21:32 No, it's for a blog article I am writing – eskimo Dec 6 '12 at 21:34 2 I presume this question is as a matter of Curiosity?

:-) – Steven Stadnicki Dec 6 '12 at 21:57 answered Dec 6 '12 at 21:37 user4594 1 Not quite: it would be $(x+1)^3 - (x-1)^3 = 100,614,152$. Edit: the answer has been corrected. – Jonathan Christensen Dec 6 '12 at 21:38 1 up vote 6 down vote Let $x$ be the number of small cubes along each edge of the large cube. Then each face of the large cube contains $x^2$ small cubes. $6x^2$ isn't the total number of cubes around the outside, though, because we're double-counting the cubes along each of the edges, so we need to subtract off $12x$. Then we aren't counting the cubes at the corners (we counted them three times--once in each face--and subtracted them three times), so we need to add back on 8.

So we have $$6x^2 -12x + 8 = 100,614,152.$$ Now this is just a simple quadratic. Combine the terms on one side and use the quadratic formula (or Wolfram Alpha ) to find that $x = 4096$. up vote 2 down vote If one big cube is divided into $n$ times smaller cubes, then there are $n^3$ cubes. Taking avay the outer layer, we are left with $(n-2)^3$ cubes. The difference is $$ n^3-(n-2)^3= n^3-(n^3-6n^2+12n-8)=6n^2-12n+8$$ and this shall equal $N=100614152$. Therefore, a good approximation for $n$ is given by $$n=\sqrt {\frac N 6}\approx 4095.0004$$ However, $n=4095$ leads to $6n^2-12n+8=100565018$, not quite your expected result.

But with $n=4096$, the result is correct: $6n^2-12n+8=100614152$. Note that trying to compute the solution of $$6n^2-12n+(8- 100614152)$$ would not have been easy due to rounding errors. Rounding errors, pfft. You can do that computation using an exact representation, like cyclotomic numbers – Ben Millwood Dec 6 '12 at 21:43 Secondinng Ben's comment, I'm not sure what rounding errors you're expecting; this isn't an equation with large amounts of cancellation since $b^2\not\approx 4ac$, so just dividing through by 6 to get $n^2-2n-16769024=0$ and then using the standard quadratic formula is fine. You have to take the square root of the eight-digit number 67076100 but that's essentially a trivial matter.

– Steven Stadnicki Dec 6 '12 at 23:41 You are right, I didn't even try it and had in min that the other solution might be $\approx0$, while of course it is $\approx -n$. – Hagen von Eitzen Dec 7 '12 at 16:21 up vote 1 down vote Let the size of the small cube be $1 \times 1 \times 1$ and size of the larger cube be $n \times n \times n$. The number of smaller cubes on the outer surface is given by $$\underbrace{2n^2}_{\text{Cover two opposite sides}} + \underbrace{2n(n-2)}_{\text{Cover next pair of opposite sides}} + \underbrace{2(n-2)^2}_{\text{Cover the remaining pair of opposite sides}}$$ answered Dec 6 '12 at 21:40 user17762 the total count of cubes increases as more and more cubes are added around an existing cube. each "level" is defined as completing the addition of an entire layer of concentric cubes that surround the previous level.

level 0 is no cubes at all level 1 is ONE cube level 2 surrounds level 1 with 8 more, 9 total cubes in each of 3 planes, total = 27 level 3 surr the 9 in l-2 /w 16 more, total 25 cubes in each of 5 planes, total = 125 level 4 surr the 25 in l-3 /w 24 more, total 49 cubes in each of 7 planes, total = 343 level 5 surr the 49 in l-4 /w 32 more, total 81 cubes in each of 9 planes, total = 729 etc... these numbers, 0, 1, 27, 125, 343, 729 each represent the total count of cubes at any given concentric level. let us call this CC_T_n which stands for the Count of Cubes _ Total _ at level n.

i figured out that: CC_T_n = ((n * 2) - 1) ^ 3 we are interested in the count of cubes required to surround a smaller block of cubes; EXACTLY what i'm doin' right here! let us call this CC_OL_n which stands for the Count of Cubes _ Outer Layer _ at level n. if you think about it, this will equal the total count of cubes in any block at level n minus the total count of cubes in the block at level n - 1; why? because, the total count at level n - 1 is the count of blocks that the count at level n must cover!

and so, CC_OL_n = CC_T_n - CC_T_n-1, which equals: (((n * 2) - 1) ^ 3) - ((((n - 1) * 2) - 1) ^ 3) working this though the consecutive levels, i got the following results: l-0 CC_T_0 = 0 l-1 CC_T_1 = 1, CC_OL_1 = 1 l-2 CC_T_2 = 27, CC_OL_2 = 26 l-3 CC_T_3 = 125, CC_OL_3 = 98 l-4 CC_T_4 = 343, CC_OL_4 = 218 l-5 CC_T_5 = 729, CC_OL_5 = 386 l-6 CC_T_6 = 1331, CC_OL_6 = 602 l-7 CC_T_7 = 2197, CC_OL_7 = 866 etc...

i typed the following string into google: 1,26,98,218,386,602,866 and i found a web site that categorizes various numeric sequences. it had a reference to a guy named Xavier Acloque with a comment "Numbers of cubes needed to completely "cover" another cube." marty wollner thetruth-machine.com Volume of a Cube - Web Formulas Current Location > Math Formulas > Geometry > Volume of a Cube Volume of a Cube Volume of a Cube: Since all of the edges of a cube are of equal length, there is no need to differentiate between the length, width and height. The volume of a cube is determined by multiplying the length of three edges of the cube. Let "a" define the length of an edge of the cube. Then the volume formula is defined as: V = a × a × a This formula is also written as V = a³. If a = 5 feet, then the volume is found like this: V = (5)³ = 5 × 5 × 5 = 125: Since each value is a measurement of feet, the volume is therefore 125 cubic feet.

Example 1: Find the volume of a solid cube shape box whose side is 13m. Solution: Given that: side a = 3m Volume of the cube is therefore: V = a³ V = 13³ V = 2197 m3 Example 2: Find the measure of volume of a cube for the given side length is 20 inches? Solution: Given that: Side a = 20 inches Volume of the cube is therefore: V = a³ Therefore, volume of a cube is 8000 in3. Example 3: Find the volume of a cube for the given side length 12.5 meter? Solution: Given that: Side a = 12.5 m V = a³ V = 1953.125 m3 Therefore, the volume of the cube is 1953.125 cubic meter. Example 4: A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to the sum of the surface areas of the smaller cubes?

Solution: The volume of the larger cube = 53 = 125 cm3. The volume of each of the smaller cubes = 13 = 1 cm3. Therefore, one would get 125 smaller cubes out of the lager cube. The surface area of the larger cube = 6a2 = 6(52) = 6x25 = 150 cm2. The surface area of each of the smaller cubes is: 6(12) = 6 cm2. The total surface area of all the smaller cubes is: 125 × 6 = 750 cm2. Therefore, the ratio is: 150: 750 = 1: 5 Example 5: A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cubes? Solution: Volume of the large cube = (33 + 43 + 53) = 216 cm3. Let the edge of the large cube be a.

a3 = 216 a = 6 cm Required ratio = total surface area of the smaller cubes / the surface area of the larger cube Required ratio = (6 × (32+42+52)) : (6 × 62) = 25:18 Example 6: A cube has a surface area of 54 square centimeters. What is the volume of the cube? Solution: The surface area of the cube is: SA = 6a2 Thus: a2 = SA/6 = 54/6 = 9 and a = 3 cm The volume of the cube is: V = a3 Cubes Tests Cubes A cube is a 3-dimensional diagram with all sides equal. If we divide it into the size (1⁄n)th part of its side, we get n3 smaller cubes. Shown below is a cube which is painted on all the sides and the cut into (1⁄4)th of its original side. Some observations: A cube has 6 faces, 12 edges and 8 corners. We can see that the cubes which got all the three sides painting lies at the corners.

So the number of cubes which got painted all the three sides is equal to 8. Cubes with 2 sides painting lie on the edges (see the diagram). But the cubes which are on the left and right side of the edge matches with the corners. So we have to substract these two cubes from the number of cubes lying on the edge to get the number of cubes with 2 sides painting. Cubes with 1 side painting lies on the surfaces. Since, the top row, bottom row, left column, and right column matches with the edges, We must exclude these cubes while calculating the single side painted cubes.

The following rules may be helpful: If a cube is divided into the size $\left( {\displaystyle\frac{{\rm{1}}}{{\rm{n}}}} \right)^{{\rm{th}}} $ of its original side after get painted all the sides, Then Total number of cubes = ${\rm{n}}^3 $ Cubes with 3 sides painting = 8 Cubes with 2 sides painting = $12 \times (n - 2)$ Cubes with 1 sied painting = ${\rm{6 \times (n - 2)}}^{\rm{2}} $ Cubes with no painting = ${\rm{(n - 2)}}^{\rm{3}} $ Solved Examples (Level - 1) 1. A cube whose two adjacent faces are colored is cut into 64 identical small cubes. How many of these small cubes are not coloured at all? Assume the top face of the cube and its right side are colored green and orange respectively. Now If we remove the colored faces, we left with a cuboid, whose front face is indicated with dots. So on the front face there are 9 cubes, and behind it lies 4 stacks.

So total 9 x 4 = 36 2. A cube, painted yellow on all-faces is cut into 27 small cubes of equal size. How many small cubes got no painting? Assume we have taken out the front 9 cubes. Then the cube looks like the one below. Now the cube which is in the middle has not got any painting. The cubes on the Top row, bottom row, left column and right column all got painting on atleast one face. Alternative method: Use formula: ${\rm{(n - 2)}}^{\rm{3}} $ Here n = 3 So ${\rm{(3 - 2)}}^3 $ = 1 3. All surfaces of a cube are colored. If a number of smaller cubes are taken out from it, each side 1/4 the size of the original cube's side, Find the number of cubes with only one side painted. The original (colored) cube is divided into 64 smaller cubes as shown in the figure. The four central cubes on each face of the larger cube, have only one side painted. Since, there are six faces, therefore total number of such cubes = 4 x 6 = 24.

Alternative Method: Use formula : ${\rm{6 \times (n - 2)}}^{\rm{2}} $ = ${\rm{6}} \times {\rm{(4 - 2)}}^2 $ = 24 Level - 2 4. Directions: One hundred and twenty-five cubes of the same size are arranged in the form of a cube on a table. Then a column of five cubes is removed from each of the four corners. All the exposed faces of the rest of the solid (except the face touching the table) are coloured red. Now, answer these questions based on the above statement: (1) How many small cubes are there in the solid after the removal of the columns? (2) How many cubes do not have any coloured face? (3) How many cubes have only one red face each? (4) How many cubes have two coloured faces each? (5) How many cubes have more than 3 coloured faces each? The following figure shows the arrangement of 125 cubes to form a single cube followed by the removal of 4 columns of five cubes each.

When the corner columns of the original cube are removed , and the resulting block is coloured on all the exposed faces (except the base) then we get the right hand side diagram. We labelled the various columns from a to u as shown in the figure (1): Since out of 125 total number of cubes, we removed 4 columns of 5 cubes each, the remaining number of cubes = 125 - (4 x 5) = 125 - 20 = 105. (2): Cubes with no painting lie in the middle. So cubes which are blow the cubes named as s, t, u, p, q, r, m, n, o got no painting. Since there are 4 rown below the top layer, total cubes with no painting are (9 x 4) = 36. (3): There are 9 cubes namaed as m, n, o, p, q, r, s, t and u in layer 1, and 4 cubes (in columns b, e, h and k) in each of the layers 2, 3, 4 and 5 got one red face.

Thus, there are 9 + (4 x 4) = 25 cuebs. (4) the columns (a, c, d, f, g, i, j, l) each got 4 cubes in the layers 2, 3, 4, 5. Also in the layer 1, h, k, b, e cubes got 2 faces coloured. so total cubes are 32 + 4 = 36 (5): There is no cube in the block having more than three coloured faces. There are 8 cubes (in the columns a, c, d, f, g, i, j and l) in layer 1 which have 3 coloured faces. Thus, there are 8 such cubes. Thus, there are 8 such cubes. 5. Directions: A cube of side 10 cm is coloured red with a 2 cm wide green strip along all the sides on all the faces. The cube is cut into 125 smaller cubes of equal size. Answer the following questions based on this statement: (1) How many cubes have three green faces each? (2) How many cubes have one face red and an adjacent face green?

(3) How many cubes have at least one face coloured? (4) How many cubes have at least two green faces each? Clearly, upon colouring the cube as stated and then cutting it into 125 smaller cubes of equal size we get a stack of cubes as shown in the following figure. The figure can be analysed by assuming the stack to be composed of 5 horizontal layers. (1): All the corner cubes are painted green. So there are 8 cubes with 3 sides painted green. (2): There is no cube having one face red and an adjacent face green as all the green painted cubes got paint on atleast 2 faces. (3): Let us calculate the number of cubes with no painting. By formula, $\left( {{\rm{n - 2}}} \right)^{\rm{3}} $ = $\left( {{\rm{5 - 2}}} \right)^{\rm{3}} $ = 27 Therefore, there are 125 - 27 = 98 cubes having at least one face coloured. (4): From the total cubes, Let us substract the cubes with red painting, cubes with no painting.

125 - (9 x 6) - 27 = 44 3D Geometry, Shape and Space :: Cubes : nrich.maths.org Partly Painted Cube Stage: 4 Challenge Level: Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use? Holes Stage: 1 and 2 Challenge Level: I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns? Painted Cube Stage: 3 Challenge Level: Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces? The Third Dimension Stage: 1 and 2 Challenge Level: Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper? A Puzzling Cube Stage: 2 Challenge Level: Here are the six faces of a cube - in no particular order.

Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube? Stage: 3 and 4 Challenge Level: In a three-dimensional version of noughts and crosses, how many winning lines can you make? Nine Colours Stage: 3 and 4 Challenge Level: You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour. Cubes Cut Into Four Pieces Stage: 1 Challenge Level: Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set? Stage: 1 and 2 Challenge Level: Investigate the number of faces you can see when you arrange three cubes in different ways. Changing Areas, Changing Volumes Stage: 3 Challenge Level: How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?

Stage: 1 and 2 Challenge Level: Can you create more models that follow these rules? Drilling Many Cubes Stage: 3 Challenge Level: A useful visualising exercise which offers opportunities for discussion and generalising, and which could be used for thinking about the formulae needed for generating the results on a spreadsheet. Start Cube Drilling Stage: 1 Challenge Level: Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them? Painted Faces Stage: 2 Challenge Level: Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they? Cube Drilling Stage: 2 Challenge Level: Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them? Cubic Net Stage: 4 and 5 Challenge Level: This is an interactive net of a Rubik's cube.

Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo! Interpenetrating Solids Stage: 5 Challenge Level: This problem provides training in visualisation and representation of 3D shapes. You will need to imagine rotating cubes, squashing cubes and even superimposing cubes! Cheese Cutting Stage: 5 Challenge Level: In this problem we see how many pieces we can cut a cube of cheese into using a limited number of slices. How many pieces will you be able to make? Stage: 2, 3 and 4 A description of how to make the five Platonic solids out of paper. Making Maths: Link-a-cube Stage: 2 Challenge Level: Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die. Classic Cube Stage: 5 Challenge Level: The net of a cube is to be cut from a sheet of card 100 cm square. What is the maximum volume cube that can be made from a single piece of card?

Inside Out Stage: 4 Challenge Level: There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . . Dice, Routes and Pathways Stage: 1, 2 and 3 This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . . Thinking 3D Stage: 2 and 3 How can we as teachers begin to introduce 3D ideas to young children? Where do they start? How can we lay the foundations for a later enthusiasm for working in three dimensions? Cubic Rotations Stage: 4 Challenge Level: There are thirteen axes of rotational symmetry of a unit cube. Describe them all. What is the average length of the parts of the axes of symmetry which lie inside the cube?

Classifying Solids Using Angle Deficiency Stage: 3 and 4 Challenge Level: Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry Cubist Cuts Stage: 3 Challenge Level: A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer? Dicey Stage: 2 Challenge Level: A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue? Green Cube, Yellow Cube Stage: 2 Challenge Level: How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 cube that is green all over AND a 2 x 2 cube that is yellow all over? Christmas Boxes Stage: 3 Challenge Level: Find all the ways to cut out a 'net' of six squares that can be folded into a cube.

Icosian Game Stage: 3 Challenge Level: This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at. Counting Triangles Stage: 3 Challenge Level: Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether? Take Ten Stage: 3 Challenge Level: Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3. . . . How Many Dice? Stage: 3 Challenge Level: A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find. . . .

Tic Tac Toe Stage: 3 Challenge Level: In the game of Noughts and Crosses there are 8 distinct winning lines. How many distinct winning lines are there in a game played on a 3 by 3 by 3 board, with 27 cells? Painting Cubes Stage: 3 Challenge Level: Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours? Four Points on a Cube Stage: 5 Challenge Level: What is the surface area of the tetrahedron with one vertex at O the vertex of a unit cube and the other vertices at the centres of the faces of the cube not containing O? Plane to See Stage: 5 Challenge Level: P is the midpoint of an edge of a cube and Q divides another edge in the ratio 1 to 4. Find the ratio of the volumes of the two pieces of the cube cut by a plane through PQ and a vertex. All in the Mind Stage: 3 Challenge Level: Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely.

Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface. . . . Christmas Presents Stage: 2 Challenge Level: We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use? Quandaries & Queries at Math Central How many diagonals does a cube have? Answered by Harley Weston. 2014-01-15 From Bob: Rick has five cubes. When he arranges them from smallest to largest, the difference between the heights of any two neighbouring cubes is 2 cm. The largest cube is as high as a tower built from the two smallest cubes. How high is a tower built from all five cubes? Answered by Penny Nom. 2013-08-22 From Dan: I am not a mathematician. This seems to me an intuitively simple enough problem that I very much need an answer to from someone who's mathematics are better than mine. Please help. The question is: for a tesseract of side length = 1 what is the distance of the center of each cube from the center of the tesseract ?

I think I have calculated the distance of each vertex from the center, and of the center of each edge from the center, but the question above baffles me. (anyone not having a clue what I am talking about can brush up here ) Thanks in advance - Dan V Answered by Robert Dawson. 2013-04-01 From Shankar: Every vertex of a cube is assigned a number +1 or -1 . Every face has a number that is the product of all the numbers in its corners. Then the 14 numbers are summed up ( all the vertices and faces ). Can the sum be 0? Answered by Chris Fisher. 2012-09-04 From alexis: a cube has one face that is equal to the total surface area of another cube. Find the ratio of their volumes Answered by Penny Nom. 2012-07-07 From jake: a storage tank is in the form of a cube. when it is full of water,the volume of water is 15.625 m cube. if the present depth of water is 1.3m, find the volume of water already used from tank Answered by Penny Nom.

2012-05-13 From Pragun: Three metallic cubes whose edges are in the ratio 3:4:5 are melt to form a single cube whose diagonal is 12*square root of 3. What are lengths of the edges(in cm) of the three cubes Answered by Penny Nom. 2012-01-23 From Gelo: What are the largest volume and total surface area of a cube that may be inscribed inside a sphere whose radius is 5 kilometers. Answered by Walter Whiteley. A pattern is built with cubes. The first item is 1 cube. The second item is a block of 8 cubes. The third item is a block of 27 cubes. If the pattern is continued, how many cubes are needed for the fourth and fifth? Answered by Penny Nom. 2010-11-24 From Ali: hi every one i have a problem with cube they told me to write a program that determine if a point is inside a cube so i need the equation of the cube to do the comparison.

in sphere it is easy sqrt((x-xp)+(y-yp)+(z-zp))<=radios if u please could help me Answered by Robert Dawson. 2010-05-22 From Anad: how can we prove a^3 - b^3 is equal to (a-b)(a^2+ab+b^2)? Answered by Penny Nom. how to derived the total surface area of a cube and rectangular prism using geoboard?? Answered by Robert Dawson. 2009-02-10 From Rebecca: I need to know the names of solid figures. I have several pictures that I need to answer what type they are. Thanks, Rebecca 3rd grade Answered by Penny Nom. 2008-12-06 From rohan: A CYLINDER IS WITHIN THE CUBE TOUCHING ALL THE VERTICALS FACES . A CONE IS INSIDE THE CYLINDER.IF THEIR HEIGHT ARE SAME WITH SAME BASE ,FIND THE RATIO OF THEIR VOLUMES. Answered by Janice Cotcher.

2008-11-19 From Neji: How do you factor (y-z) (y+z) (y^4+y^2z^2+z^4) and get (y+z)(y^2-yz+z^2) (y-z) (y^2+yz+z^2) as the answer? Answered by Harley Weston. 2008-09-09 From Dave: In an urn, there are 80 objects of two kinds: cubes (C) and balls (B). An object can be either red (R) or green (G). Note that all the four combinations are possible and that the number of cubes is not necessarily equal to the number of balls. Similarly, the number of red objects is not necessarily equal to the number of green objects. Someone tells us that in the urn there are 20 red cubes, 50 balls, and 30 red objects. An object is randomly selected from the urn. (a). What is the probability that a green ball is selected? (b). If we know that a cube has been selected, what is the probability that it's red? (c).

If we know that a red object has been selected, what is the probability that it's a cube? Answered by Harley Weston. 2008-08-25 From Mhiko: how many hidden faces of a cubes are there in a 5 cubes in a row? how many hidden faces of a cubes are there in a 10 cubes in a row? how many hidden faces of a cubes are there in a 15 cubes in a row? how many hidden faces of a cubes are there in a 20 cubes in a row? please show me the solution or formula.... Answered by Janice Cotcher. 2008-07-17 From Pete: Is the only way to find a cube root of a really big number guess and check, as i read in other questions, or is there another way without a calculator? Answered by Harley Weston. 2008-07-16 From Steven: A cube is inscribe in a right cone of radius 2 and height 5. What is the volume of the cone? Answered by Victoria West and Harley Weston. 2008-05-24 From cailtlin: hi..

if the surface area of a cube is 384 cm^2, how could i find the length of one edge? thank you Answered by Penny Nom. 2008-05-19 From Xiu: I dont get this question.. Write "the cube of -2y" in exponential form. I know the answer is -(2y)^2 but i really don't understand why. Can you explain how to do this whole problem for me? Answered by Leeanne Boehm. From Tom: (a) By plotting suitable graphs, estimate to one decimal place the cube root of 270. (b) With reference to your answer to part (a), use 8 iterations of a Bisection Search to refine your estimate. Use the nearest whole numbers either side of your estimate from part (a) as starting values. (c) Using either of your starting values from part (b) as first guess, use the Newton-Raphson method to find the true value of the root (to 6 decimal places). Repeat using the other starting value from part (b) and compare the two results. Answered by Harley Weston. Given a Cube's diagonal, how does one find the edge of the cube.

Answered by Stephen La Rocque. 2008-01-30 From Amanda: It has been a really long time since I was in Algebra and I can't remember how to factor cubes such as x^3 +81 or subtracting/adding fractions with variables such as [1/(x+h)+2]-[1/x+2]. Please help!!! Answered by Penny Nom. 2008-01-16 From Bill: A student asked me where did the "difference of cubes" and "sum of cubes" come from. I did not have an answer for her. She is very bright and understands how they work but wanted to know where they derived from. Any help you can offer would be great. Thanks Answered by Stephen La Rocque. 2008-01-12 From Sadie: can you help me to find out how to cube a number example (6 cubed / by4) =54 what is cube or how do you cube something Answered by Penny Nom.

2008-01-03 From Justin: I have one cubic yard of liquid that I want to convert to a cylindrical volume with the inside dimensions being 3/4 of an inch. I am trying determine what the height/length would be to set these equal. i.e. What length of hose will I need (with an inside diameter of 3/4") in order to accommodate exactly one cubic yard of liquid? Answered by Penny Nom. 2007-11-27 From Ashutosh: A rectangular block measuring 10 units by 8 units by 6 units is made up of cubes measuring 1 unit on a side. The base of the block is 10 units by 8 units. The outside of the block other than the base is painted red. How many of the unit cubes have exactly one face painted red? Answered by Stephen La Rocque and Penny Nom.

2007-09-21 From Yvonne: The numbers 756 and 72, expressed as products of prime factors, are 756 = 2ï¿½ x 3ï¿½ x 7 and 72 = 2ï¿½ x 3ï¿½ Use these result to find, the smallest integer, x, such that 756x is a perfect cube. Answered by Penny Nom. 2007-09-11 From Justin: What percent of the volume of a cube is occupied by the largest possible sphere centered in that cube? Answered by Stephen la Rocque. 2007-07-30 From Arul: what is the easiest way to find the number which is both a square and a cube? the numbers i know are 64 and 729 which is both a sqr and a cube. i took long time to solve this.. is there any easier way? Answered by Steve La Rocque.

2007-06-23 From Leah: I am having trouble finding the equation for this problem.: What is the volume of a cube with diagonals of length 6 sqrt(3) cm? answer: (BLANK) cm3 Answered by Penny Nom. 2007-04-11 From Bethany: If I am filling a hole in the shape of a cube with 64 cubic yards of dirt, how many feet deep will my hole be. Answered by Stephen La Rocque. 2007-01-31 From Jacqui: How would you find the answer of a cube root backwards. For example: 8000 but backwards. Like, what number made that and how would you do it? Answered by Penny Nom. 2006-12-12 From Liz: What is the volume of the solid remaining if a unit cube has a hole drilled thru one face to the opposite side and the hole that is drilled is a cylinder of unit diameter. Then the cube is rotated and an identical hole is drilled from an untouched face to the opposite side. Then the cube is rotated and an identical hole is drilled between the last two untouched faces.

This will result in the cube vertices and the remaining volume of the cube falling into 8 parts. What is the total volume of these 8 parts. How is this volume calculated? Answered by Penny Nom. 2006-11-10 From Leeza: How many dump trucks (I believe the standard bed size is 16'L x 8'W x 4'D) would it take to hold one trillion sugar cubes (which I believe are approximately 2cm in L, W and D)? Answered by Penny Nom. 2006-11-09 From Lukas: Given a cube and a cross diagonal, what is the largest size sphere that fits in the cube and does not touch or intersect the cross diagonal? Answered by Steve La Rocque, Penny Nom and Walter Whiteley. Given the diameter of the sphere 10cm. find the largest cube inscribe in the sphere. Answered by Stephen La Rocque. 2006-05-19 From Maria: I am trying to build a box with an interior of 1.26 cu. feet with all sides equal. Answered by Stephen La Rocque and Penny Nom.

2006-03-10 From Iban: cube cheese is 4cm wide, 4cm long, 4cm high. three faces of the cube meet in the corner covers thin layers of wax. The cheese is then cut two, then cut 64 small cubes, which is the length 1cm. How many of these cubes have no wax of them? Answered by Stephen La Rocque. 2005-10-19 From Damian: A sphere passes through the eight corners of a cube side 10cm. Find the volume of the sphere. Answered by Penny Nom. 2005-03-06 From Brett: A cube has a volume of 64 cubic inches. What is the length of segment AB? Segment AB is a straight line from the top left corner of the cube to the lower right bottom corner Answered by Penny Nom. 2005-01-17 From Jake: I have one for you that's got me stumped. Is it possible to calculate the dimensions of a square if I have the cubic feet? Say I know the package to be 180 cubic feet. Answered by Penny Nom.

2004-12-22 From Andrea: What is the smallest positive interger by which 252 can be multipled so the result is a perfect cubed? Answered by Penny Nom. "a"cubed minus "b"cubed equal (a-b) times ("a"squared plus "ab" plus "b"squared)? I know this is a formula, but why is it true? Answered by Penny. 2004-11-23 From Anthony: You are working with a power saw and wish to cut a wooden cube 3-inches on aside into 27 1-inch cubes. You can do this by making six cuts through the cube keeping the pieces together in the cube shape. Can you reduce the number of necessary cuts by rearranging the pieces after each cut? Answered by Chris Fisher. 2004-10-26 From A parent: How do you solve the problem of finding the cubed root of (17 to the power of 3). Can you show me each step and if you have a visual representation of this it would be very helpful. Also can you show a step by step of finding the cubed root of 27.

Visuals help a lot Answered by Penny Nom.

Question: What is the minimum number of smaller cubes required to make a larger cube?
Answer: EIGHT