Question

dimensions of a rectangular prism as shown below: Length:2 1/4 feet. Width: 1 foot. Height:1 1/4 feet. The lengths of the side of a small cube or 1/4 for each. Part A: how many small cubes can be packed in a rectangular prism? Show your work. Part B: use the answer obtained in part a to find the volume of a rectangular prism in terms of the small cube in unit cube.

Answer 1

Explanation:

In this case we will use the formula V= length × width × height

so, V= 2 1/4 × 1 × 1 1/4

=2 1/4 × 1 1/4

= 9/4 × 5/4

= 45/16

=2 13/16 cubic feet is the full capacity of the rectangular prism

then get the volume of the cube so, we will use the formula V= side times side times side

so, V= 1/4 times 1/4 times 1/4

V= 1/8 times 1/4

V= 1/32 cubic is the volume of the cube

then we will divide the full capacity of the rectangular prism to the volume of the cube

so, 2 13/16 divided by 1/32

so, 2 13/16 times 32/1

so, 45/16 times 32/1

=1,440/16

=90 small cubes can be packed in a rectangular prism in Part A

so, in Part B

V= 2 1/4 × 1 × 1 1/4

=2 1/4 × 1 1/4

= 9/4 × 5/4

= 45/16

=2 13/16 cubic feet is the volume of the rectangular prism