# Cups A and B are cone shaped and have heights of #32 cm# and #14 cm# and openings with radii of #15 cm# and #12 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?

##### 3 Answers

height =

#### Explanation:

Volume cone =

We only need to know which one is bigger, not the actual volumes.

We can therefore ignore

By inspection we can see that :

So A will not overflow, but how high will the water reach?

The water in A and the whole cup A are similar figures.

Therefore we can compare the ratio of the cubes of the heights with the ratio of their volumes.

Cup A's height will be 7.68cm

#### Explanation:

Volume of cone

A

Vol. A

Vol.B

New vol cup A=

a. not overflow

b. height of cup A = 8.96cm

#### Explanation:

where r = radius and h = height

so, cup A wont overflow because it is bigger than cup B.

let say T is the height of cup A when content in cup B poured to cup A.

Va = Vb