# Cups A and B are cone shaped and have heights of #12 cm# and #15 cm# and openings with radii of #6 cm# and #4 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

Feb 23, 2016

Cup A will not overflow and will fill up to a height of

#### Explanation:

Volume of a cone whose radius is

Hence volume of Cup A is

and volume of Cup B is

As volume of Cup B is less than that of A, when cup B is full and its contents are poured into cup A, cup A will not overflow.

Let Cup A be filled till height

or