# Cups A and B are cone shaped and have heights of #24 cm# and #23 cm# and openings with radii of #11 cm# and #9 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 12, 2016

#### Explanation:

Volume of a cone is given by

Volume of cone A is

Volume of cone B is

It is obvious that when contents of a full cone B are poured into cone A, it will not overflow. Let it reach where upper circular surface will form a circle of radius

then the relation becomes

So equating