# Cups A and B are cone shaped and have heights of #33 cm# and #27 cm# and openings with radii of #13 cm# and #8 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?

##### 1 Answer

Mar 5, 2016

Cup A will not overflow because

Cup A will be filled up to

#### Explanation:

Compute for the volumes of cups A and B first.

The formula for cone

For cup A

For cup B

We need 2 equations to solve for unknown height with

For cup A, we need the ratio of Radius to Height:

and

Using volume of

God bless...I hope the explanation is useful.