Question

Cups A and B are cone shaped and have heights of `32 cm` and `37 cm` and openings with radii of `12 cm` and `19 cm`, 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?

Answer 1

Cup A will overflow

Explanation:

Volume of a cone is given by `v = 1/3pir^2h`
where h is the height and r is the radius of the cone

Volume of Cup A: `1/3pir^2h = 1/3pitimes12^2times32 = 1536pi`

Volume of Cup B: `1/3pir^2h = 1/3pitimes19^2times37=4452 1/3pi`

If Cup B is full, which has a volume of `4452 1/3pi` which is larger than the volume of Cup A which is `1536pi`. Therefore, Cup A will overflow.