Contemporary Mathematics : Measurement Units

Question

You want to put a 6 inch thick layer of topsoil for a new 19 ft by 14 ft garden. The dirt store sells by the cubic yard. How many cubic yards will you need to order?

You need to order______  cubic yards of topsoil.

Answer 1

Hi Kiara..

You want to put a 6 inch thick layer of topsoil for a new 19 ft by 14 ft garden. The dirt store sells by the cubic yard. How many cubic yards will you need to order?

You need to order______ cubic yards of topsoil.

Given: 6 inches of topsoil 19 ft x 14 ft garden

Find: Cubic Yards.

This problem deals with volume and unit conversion.

First you need to find the volume of topsoil you need.

The units for the dimensions are 19 ft by 14 ft and 6 inches deep.

This is the shape of a rectangular prism.

The volume is length times width times height.

Since the dimensions are in feet and inches, I'll change the height from inches to feet.

6 inches x [(1 foot) / 12 inches] = 0.5 feet

So

19 ft x 14 ft x 0.5 ft = 133 ft³

Now you need to convert cubic feet into cubic yards.

1 yard = 3 feet.

133 ft³ x [1 yard / 3 ft]³= 133/27 = 4.9 cubic yards

Hope this helps. Let me know if you have any more questions!