# Cups A and B are cone shaped and have heights of #33 cm# and #37 cm# and openings with radii of #10 cm# and #13 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

#### Explanation:

We need to find and compare the Volumes of A and B.

Check first whether they are similar in shape - this would make some of the calculations easier.

Are the sides in the same ratio?

By inspection we can see that

Therefore A will not overflow but we need the height.

The cone formed by the water in A and the whole cone of A are similar in shape.

The ratio of the cubes of the heights is equal to the ratio of the volumes.