Question

Instructions
Search your home for a rectangular prism. Some examples are a cereal box, a CD case, or a coffee table. Measure your prism using appropriate units, such as inches, centimeters, or feet.

Complete the following. Show all work for calculations.

1. List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).
2. Describe the shape of the cross section when the box is cut parallel to the base.
3. What is the surface area of the box?
4. What is the surface area of the box if it is scaled up by a factor of 10?
5. What is the volume of the box?
6. What is the volume of the box if it is scaled down by a factor of
1/10?

Answer 1

Answer:

Using a cereal box, the dimensions are 8 inches wide by 12 1/8 inches tall by 1 3/4 inches deep.

Parallel to the base it would be a rectangle 8 inches x 1 3/4 inches.

Surface area = 2 x (12 1/8 x 8) + 2 x (8 x 1 3/4) + 2 x ( 12 1/8 x 1 3/4) = 194 + 28 + 42 7/16 = 264 7/16 square inches.

Surface area if scaled up by a factor of 10:

10^2 = 100

264 7/16 x 100 = 26,443 3/4 square inches.

Volume =  8 x 12 1/8 x 1 3/4 = 169 3/4 cubic inches.

Volume scales down by 1/3:

1/3^3 = 1/27

169 3/4 x 1/27 = 6 31/108 cubic inches.