Suppose we wanted to make a concrete bench like the one shown in this picture. If we know that the finished bench has a volume of 10 ft3 and a surface area of 44 ft2 we can use this information to solve problems about the bench.
- How much does the bench weigh?
- How long does it take to wipe the whole bench clean?
- How much will the materials cost to build the bench and to paint it?
To figure out how much the bench weighs, we can use its volume, 10 ft3. Concrete weighs about 150 pounds per cubic foot, so this bench weighs about 1,500 pounds, because $10 \boldcdot 150 = 1,\!500$.
To figure out how long it takes to wipe the bench clean, we can use its surface area, 44 ft2. If it takes a person about 2 seconds per square foot to wipe a surface clean, then it would take about 88 seconds to clean this bench, because $44 \boldcdot 2 = 88$. It may take a little less than 88 seconds, since the surfaces where the bench is touching the ground do not need to be wiped.
Would you use the volume or the surface area of the bench to calculate the cost of the concrete needed to build this bench? And for the cost of the paint?