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?

Question

asked Jan 13, 2021 87.2k views

1 Answer

MattCrum · Answer 1 · 2021-01-18T14:46:38+0000

Answer:

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

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