options: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Solve real-world and mathematical problems involving area, surface area, and volume.

Visualize relationships between two-dimensional and three-dimensional objects.

Make geometric constructions.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Apply trigonometry to general triangles.

Classify two-dimensional figures into categories based on their properties.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Prove theorems involving similarity.

Understand and apply the Pythagorean Theorem.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Understand similarity in terms of similarity transformations.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Analyze, compare, create, and compose shapes.

Find arc lengths and areas of sectors of circles.

Experiment with transformations in the plane.

Translate between the geometric description and the equation for a conic section.

Define trigonometric ratios and solve problems involving right triangles.

Understand and apply theorems about circles.

Explain volume formulas and use them to solve problems.

Use coordinates to prove simple geometric theorems algebraically.

Apply geometric concepts in modeling situations.

Reason with shapes and their attributes.

Prove geometric theorems.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Understand congruence in terms of rigid motions.
problem_activity: Problem 1
A small box measures 5 in. across, 8 in. deep, and 6 in. tall. A book that measures 5
$$\times$$
8
$$\times$$
1 in. fits perfectly into the bottom of the box.
[IMG]
a.   What is the volume of one book? How many books will fit into the box? What is the volume of all of the books that will fit into the box?
b.   What is the volume of the box? How is this related to the volume of one book?
c.   A medium box measures 12 inches tall. A different book with dimensions 8
$$\times$$
10
$$\times$$
1 in. fits perfectly into the bottom of the medium box. What is the volume of the medium box?
Problem 2
The same rectangular prism is positioned in two different ways, as shown below. For each prism, use the rectangular face that the prism is “sitting on” as the base of the prism.
[IMG]
For each prism, find the area of the base and multiply by the height. Show that this is the same volume as when all three dimensions are multiplied together.
Problem 3
A rectangular prism has a base area of
$${4{3\over8}}$$
inches
$${^2}$$
, a width of
$$1 \frac{1}{4}$$
inches, and a height of
$${6 {1\over2}}$$
inches. Kirby writes the equation
$$V=4\frac{3}{8}\times1\frac{1}{4}\times6\frac{1}{2}$$
to represent the volume of the prism.
Do you agree with Kirby's equation? Explain and find the volume of the prism.


correct_option_index: 1