A pawn shop owner offers a gold coin of diameter 3 cm for the same price as two gold coins (of the same thickness) of diameter 2 cm. Which has more gold, the single coin or the two coins together?
Answer: Assuming that all the coins are circular and have the same thickness, the volume of gold in each coin is π r2 where r is the radius of the coin, times the thickness t. The single coin has r = 3/2, so its volume is π(9/4)t. Each of the smaller coins has volume π (1)2t. The two coins together have volume 2π t, which is less than the volume of the single coin, so the single coin has more gold.
