Hints and solutions to Draw a Picture #9

A straight concrete sidewalk is to be 3 feet wide, 60 feet long, and 3 inches thick. How many cubic yards of concrete must a contractor order for the sidewalk if concrete must be ordered in a whole number of yards?

  • A diagram always helps. Here is a picture of the planned sidewalk, with the length, width and thickness indicated:

  • The lengths are given in different kinds of units (inches, feet) and the concrete is sold in different units still (cubic yards). So first, we have to settle on one kind of unit of length.
  • So, since we need to order concrete in cubic yards, let's do the whole calculation in yards.
  • Since 1 yard = 3 feet, the sidewalk is to be 1 yard wide and 20 yards long. Also, 1 yard = 36 inches, thus the sidewalk is to 1/12 yard thick.
  • As shown in the figure, the shape of the sidewalk is that of a rectangular box. The volume of such a box is length x width x height, so the total volume of the sidewalk is 1 x 20 x 1/12 = 20/12 = 5/3 = 1.666.. cubic yards.
  • Finally, since he must order a whole number of cubic yards, the contractor will need to order 2 cubic yards of concrete.