A rectangular prism has a length of 20 in., a width of 2 in., and a height of 3(1)/(4) in. The prism is filled with cubes that have edge lengths of (1)/(4) in. How many cubes ar…

Question

A rectangular prism has a length of 20 in., a width of 2 in., and a height of 3
`(1)/(4)` in.

The prism is filled with cubes that have edge lengths of
`(1)/(4)` in.

How many cubes are needed to fill the rectangular prism?

Answer 1

Calculate the volume of both the prism and the cubes:

Prism:

Volume = 20 x 2 x 3.25 = 130 cubic inches.

Volume of cube:

Volume = S^3 = 1/4^3 = 1/64 ( 0.015625)

Divide the area of the prism by the area of the cube:

130 / 1/64 = 130 * 64 = 8,320

It would take 8,320 cubes to fill the prism.