Question

You want to put a 5 inch thick layer of topsoil for a new 30 ft by 18 ft garden . The dirt store sells by the cubic yards . How many cubic yards will you need to order ? The store only sells in increments of 1/4 cubic yards.

Answer 1

8.5 cubic yards

Explanation:

The volume of topsoil can be calculated by multiplying the area of the garden by the height of the soil.

As the height of the soil is given in inches, first convert this into feet by dividing the inches by 12:

`\implies \sf 5\;inches=(5)/(12)\;ft`

Therefore:

`\begin{aligned}\sf \implies Volume\;of\;soil & = \sf Width * Length * Height\\\\&= \sf 18 * 30 * (5)/(12)\\\\& = \sf 540 * (5)/(12)\\\\& = \sf (540 * 5)/(12)\\\\& = \sf (2700)/(12)\\\\& = \sf 225\;ft^3\end{aligned}`

Therefore, you would need 225 ft³ of topsoil.

To convert cubic feet into cubic yards, divide the cubic feet by 27:

`\implies \sf 225\;ft^3=(225)/(27)\;yd^3=8.33\;yd^3\;(2\:d.p.)`

If the store only sells the topsoil in increments of ¹/₄ cubic yards, then we need to round up to the nearest quarter which would be 8.5 cubic yards.