Question

A building contractor is building a backyard playground and wishes to put down rubber mulch to provide safety from falls. The contractor wishes to put the mulch in a pit in the shape of a rectangular solid 21 feet​ long, 14 feet​ wide, and 9 inches deep.

​a) Determine the​ volume, in cubic​ feet, of mulch the contractor will need.
​b) If mulch costs ​$11 per cubic​ foot, what will the cost of mulch​ be?

Answer 1

`a)220.5\ ft^3\\\\b)\$2,425.5`

Explanation:

a) The volume of a rectangular prism can be calculated by multiplying its dimensions.

In this case, you know the rectangular solid has 21 feet​ long, 14 feet​ wide, and 9 inches deep.

Since
`1\ ft=12\ in`, then its depth in feet is:

`depth=((9\ in)(1\ ft))/(12\ in)=(3)/(4)\ ft`

Therefore, its volume is:

`V=(21\ ft)(14\ ft)((3)/(4)\ ft)\\\\V=220.5\ ft^3`

b) Knowing that each cubic foot of mulch costs $11, you can calculate the total cost of the mulch the contractor needs to buy, multiplying the volume by the $11.

Then, you get:

`Total\ cost=(220.5)(\$11)=\$2,425.5`