# Cups A and B are cone shaped and have heights of #32 cm# and #12 cm# and openings with radii of #5 cm# and #6 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?

##### 2 Answers

There's no way the contents of that little cup will overflow that tall glass, and indeed it fills to height of exactly 17.28 cm.

#### Explanation:

We have the volume of a cup or cylinder of height

So there will be plenty of room in

To get the height, we solve for

#### Explanation:

Volume of a cone is given by:

First find the volumes of A and B:

Volume of A:

Volume of B:

So the contents of B will no overflow when poured into A. To find the height it will reach we solve for