Will 1 yard of topsoil cover 150 square feet at 2 inches deep?

Answer 1

Our first step must be to convert all of our measurements into the same units. It is often easiest to convert all measurements into the smallest unit given which, in this instance, is inches. Let's begin with 1 cubic yard.

1yd=36in

1yd3=46656in3

This conversion is done by cubing both values. Remember that a cubic yard has dimensions of 1yd x 1yd x 1yd. If we convert all three of those measures into inches, the dimensions are 36in x 36in x 36in. 36*36*36=46656in3. Now lets convert 150ft2 into in2.

1ft=12in

1ft2=144in2

150ft2=21600in2

Because we are working with a square measure, we square both measurements. One square foot has dimensions of 1ft x 1ft. Converting those measures into inches gives us dimensions of 12in x 12in. 12in*12in=144in2. Now we multiply 144 by 150 to give the number of square inches in 150 square feet. 144in2*150=21600in2. Now we want the volume of 21600in2 covered 2 inches deep.

21600in2*2in=43200in3.

In this case, we simply multiply the area by the depth to get volume. Now we know the volume of topsoil and the volume we need to cover both expressed in cubic inches. We need only compare the values.

46656in3 > 43200in3

One cubic yard is greater than 150 square feet at 2 inches deep, so it will cover the given area with 3456in3 to spare.