Question

T rectangular prism has a length of 2 1/2 feet, a width of 3 feet, and a height of

1 1/2 feet. Unit cubes with side lengths of 1/2 foot are added to completely
fill the prism with no space remaining. What is the volume, in cubic feet, of the right rectangular
prism?
Show your work.​

Answer 1

Volume of the rectangular prism is
`11(1)/(4)` cubic feet.

The number of small cubes required is 90.

Step-by-step explanation:

The rectangular prism has a length of
`2(1)/(2)` feet, a width of 3 feet, and a height of
`1(1)/(2)` feet.

Now, the volume of the rectangular prism will be
`(2(1)/(2) * 3 * 1(1)/(2)) = ((5)/(2) * 3 * (3)/(2)) = (45)/(4)` cubic feet i.e.
`11(1)/(4)` cubic feet. (Answer)

Now, the volume of the small unit cubes of side lengths of
`(1)/(2)` feet will be
`((1)/(2))^(3) = (1)/(8)` cubic feet.

So, the number of small cubes required to fill the large cube will be
`((45)/(4) / (1)/(8)) = 90`. (Answer)