Cups A and B are cone shaped and have heights of 32cm and 27cm and openings with radii of 12cm and 12cm, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?

1 Answer
May 24, 2018

27cm

Explanation:

Volume of a cone is given as:

13area of base×height

We can see that both have the same radii, but A has a greater height, so A has a greater volume than B.

Volume of A:

13π(144)(32)=1536π

Volume of B:

13π(144)(27)=1296π

Volume of partly filled A is equal to the volume of B:

13π(144)h=1296π

h=31296π144π=27cm

Well that's no surprise, since they both have the same radius. I would think this part of the question is incorrect.