Question

The dimensions of a rectangular prism are shown below: Length: 2 1/4 ft, Width: 1 ft Height: 1 1/4 ft The lengths of the sides of a small cube are 1/4 foot each. Part A: How many small cubes can be packed in the rectangular prism? Show your work. (5 points) Part B: Use the answer obtained in part A to find the volume of the rectangular prism in terms of the small cube and a unit cube. (5 points)

Answer 1

Answer: A. 36 small cubes

B. 36 (small ft)^3

9/16 ft^3

Explanation:

A. 2 1/4 * 1 * 1/4 =

(8+1)/4 * 1/4=

9/4*1/4=9/16.

Small cube: 1/4*1/4*1/4=1/64

9/16=

9*4/(16*4)=36/64

36/64 / 1/64=

36/64 * 64=36 small cubes

B. 36 small cubes ==> 36 (small ft)^3

2 1/4 * 1 * 1/4 =

(8+1)/4 * 1/4=

9/4*1/4=9/16 ft^3