EXAMPLE 2.7.1

The pedestal on which a statue is raised is a rectangular concrete solid measuring 9 feet long, 9 feet wide and 6 inches high. How much is the cost of the concrete in the pedestal, if concrete costs $70 per cubic yard?

A. $34,020

B. $105

C. $315

D. $2835

SOLUTION

We need to find the volume of the pedestal, in cubic yards, and then multiply by the cost factor of $70 per cubic yard. Recall the general formula for computing the volume of a rectangular solid:

Volume = Length times Width times Height

In this case, L = 9 feet, W = 9 feet and H = 6 inches. Since we want to compute volume in cubic yards, we should convert all three measurements to yards before using the formula for volume. To convert from feet to yards we divide by 3; to convert from inches to yards we divide by 36.

Length = 9 feet = 3 yards

Width = 9 feet = 3 yards

Height = 6 inches = 6 thirty-sixths of a yard = one sixth of a yard

Now we compute the volume:

Volume = Lengh times width times height = 3 time 3 time one sixth = 1.5 cubic yards.

Finally, we multiply by the cost factor:

Cost = (1.5 cubic yards) times ($70 per cubic yard) = $105