The volume of a sphere is directly proportional to the cube of its diameter.

Question

The volume of a sphere is directly proportional to the cub of its diameter. A recipe for apple pie calls for 8 apples that are each 4in. in diameter. How many apples, each 3in. in diameter, would be needed to make this pie?

Answer 1

Volume of 8 4" diameter apples is 8k(pi)2³ and volume of n 3" diameter apples is nk(pi)1.5³.

 

Setting these equal, and cancelling the factors k(pi), we get 8(8) = 3.375n

and so n = 18.963 apples.

 

Note: this computation ignores the fact that apples must be cored to keep seeds, etc. out of the pies.