Question

The dimensions of a rectangular prism are shown below: Length 2 1/4 ft | width 1 ft | height 1 1/4 ft.

The lenghts of the sides of a small cube are 1/4 ft each.

Part A: how many small cubes can be packed in the rectangular prism? Show your work. (5 Points)
Part B: Use the asnwer 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

• See below

Explanation:

Dimensions given:

• l = 2 1/4 ft, w = 1 ft, h = 1 1/4 ft

A small cube has side of 1/4 ft

Find the number of small cubes can fit in each dimension of the prism.

Length

• 2 1/4 : 1/4 = 9/4 * 4 = 9

Width

• 1 : 1/4 = 1 *4 = 4

Height

• 1 1/4 : 1/4 = 5/4 * 4 = 5

Part A

Number of small cubes would be:

• 9*4*5 = 180

Part B

Each small cube has volume:

• V = (1/4)³ = 1/64 ft³

The volume of the prism in terms of small cubes is 180 as we found above.

The volume in terms of unit cube:

• V = 180*1/64 = 180/64 = 2 52/64 = 2 13/16 ft³ or 2.8125 ft³