Mr. Price makes cakes for special occasions. His most popular-sized cakes have a volume of 360 cubic inches. The cakes have a height, or thickness, of 3 inches, and have different whole number lengths and widths. No cakes have a length or width of 1 or 2 inches. How many different cakes, each with a different-size base, have a volume of 360 cubic inches?
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What if the 360 cubic-inch cakes are 4 inches thick and any whole number length and width are possible? How many different cakes could be made? Suppose that the cost of a cake that size is $25, plus $1.99 for every 4 cubic inches of cake. How much would the cake cost?
One company makes inflatable swimming pools that come in four sizes of rectangular prisms. The length of each pool is twice the width and twice the depth. The depth of the pools are each a whole number from 2 to 5 feet. If the pools are filled all the way to the top, what is the volume of each pool?
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