A trampoline company sells covers for several different sizes of trampolines. One trampoline has a diameter of 16 feet, and its cover sells for $180. The other trampoline has a diameter of 8 feet.

How much should the company charge for the smaller trampoline cover, in dollars, if they want it to have the same price per square foot as the larger one?

Question

A trampoline company sells covers for several different sizes of trampolines. One trampoline has a diameter of 16 feet, and its cover sells for $180. The other trampoline has a diameter of 8 feet.

How much should the company charge for the smaller trampoline cover, in dollars, if they want it to have the same price per square foot as the larger one?

anonymous · Answer

logic would force me to say, if it's half the size it should cost half as much.

directrix · Answer

Any two circles are similar. Assuming that the covers are circles, they are also similar with a scale factor of two to one or (2/1). The square of the scale factor is the ratio of the areas of the covers.
(2/1) ^ 2 = 180/x  where x is the cost of the smaller cover
4/1 = 180 / x
4x = 180
x = 45 dollars --> answer