Question

A rectangular prism has a length of 11 3/4 inches, a width of 9 1/2 inches, and a height of 8 inches. How many cubes with 1/4 inch edges can fit in the rectangular prism?

Answer 1

`57,152\ cubes`

Explanation:

we know that

The volume of a rectangular prism is equal to

`V=LWH`

we have

`L=11(3)/(4)\ in`

`W=9(1)/(2)\ in`

`H=8\ in`

step 1

Convert mixed number to an improper fractions

`L=11(3)/(4)\ in=(11*4+3)/(4)=(47)/(4)\ in`

`W=9(1)/(2)\ in=(9*2+1)/(2)=(19)/(2)\ in`

step 2

Find the volume of the rectangular prism

`V=((47)/(4))((19)/(2))(8)=893\ in^(3)`

step 3

Find the volume of the cube

The volume of the cube is equal to

`V=((1)/(4))^(3)=(1)/(64)\ in^(3)`

step 4

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

`893/(1/64)=57,152\ cubes`