Question

A company is trying to calculate the amount of

concrete that will be needed to create one concrete
block that is in the form below.
The concrete block is a rectangular prism with two
cubes cut out. The cubes have a side length of 6
inches.
What is the total volume, cubic feet, of concrete
needed to make this block?

Answer 1

`0.19\,\,cubic\,\,feet`

Explanation:

Given:

The concrete block is a rectangular prism with two cubes cut out. The cubes have a side length of 6 inches.

To find: total volume, cubic feet, of concrete needed to make this block

Solution:

Side of cube = 6 inches

Volume of cube =
`(side)^3=6^3=216\,\,cubic\,\,inches`

So, volume of two cubes = 2(216) = 432 cubic inches

Length of rectangular prism = 12 inches

Breadth of rectangular prism = 8 inches

Height of rectangular prism = 8 inches

Volume of rectangular prism = length × breadth × height =
`12(8)(8)=768 \,\,cubic\,\, inches`

Total volume of concrete needed to make this block = Volume of rectangular prism - Volume of two cubes = 768 - 432 = 336 cubic inches =
`(336)/(1728) =0.19\,\,cubic\,\,feet`

( use 1 cubic inch =
`(1)/(1728) \,\,feet`)