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

Use coordinates to prove simple geometric theorems algebraically.

Apply trigonometry to general triangles.

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

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

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

Define trigonometric ratios and solve problems involving right triangles.

Prove theorems involving similarity.

Reason with shapes and their attributes.

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

Understand and apply theorems about circles.

Understand similarity in terms of similarity transformations.

Analyze, compare, create, and compose shapes.

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

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

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

Explain volume formulas and use them to solve problems.

Make geometric constructions.

Understand congruence in terms of rigid motions.

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

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

Understand and apply the Pythagorean Theorem.

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

Experiment with transformations in the plane.

Find arc lengths and areas of sectors of circles.

Apply geometric concepts in modeling situations.

Prove geometric theorems.
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: 3