# Cups A and B are cone shaped and have heights of #25 cm# and #27 cm# and openings with radii of #12 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?

##### 1 Answer

Cup A will be filled to a height of 16.2 cm.

#### Explanation:

The volume of a cone can be found using the formula;

Here,

It seems that the volume of cup A is larger than the volume for cup B, so cup A will not overflow. Instead, the water will settle into a cone of water with some height,

We do not yet know the values of

Now we can solve for

Going back to our volume expression above, we can plug in this

The volume formula constants will cancel out, and the

The rest is algebra.