Question

A right rectangular prism's edge lengths are 2 1 2 inches, 2 inches, and 6 inches. How many unit cubes with edge lengths of 1 3 inch can fit inside the prism?

Answer 1

810 cubes

Explanation:

step 1

Find the volume of the rectangular prism

The volume of the rectangular prism is

`V=LWH`

we have

`L=2(1)/(2)\ in=2+(1)/(2)=(5)/(2)\ in`

`W=2\ in\\H=6\ in`

substitute

`V=((5)/(2))(2)(6)`

`V=30\ in^3`

step 2

Find the volume of the cube

The volume of the cube is

`V=b^3`

where

b is the length side of the cube

we have

`b=(1)/(3)\ in`

substitute

`V=((1)/(3))^3`

`V=(1)/(27)\ in^3`

step 3

Find out how many unit cubes with edge lengths of 1/3 inch can fit inside the prism

Divide the volume of the prism by the volume of the cube

`30:(1)/(27)=30(27)=810\ cubes`