Question

You want to put a 4 inch thick layer of topsoil for a new 14 ft by 31 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

5 1/2 cubic yards

Explanation:

You want the volume of a 4 inch layer of topsoil for a 14 ft by 31 ft garden to the next higher 1/4 cubic yard.

Volume

We can find the volume in cubic yards by first converting all of the dimensions to yards:

4 in = 4/36 yd = 1/9 yd

14 ft = 14/3 yd

31 ft = 31/3 yd

The volume is the product of these dimensions:

V = LWH = (1/9 yd)(14/3 yd)(31/3 yd) = 434/81 yd³ = 5 29/81 yd³

That's about 5.36 yd³. The next higher 1/4-yd³ increment is 5.5, so you will need to order 5.5 cubic yards.