# Cups A and B are cone shaped and have heights of 32 cm and 21 cm and openings with radii of 13 cm and 11 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?

Jun 28, 2016

cup B contents when poured into cup A will not cause overflow. cup A will be filled up $15.0355 C m$

#### Explanation:

Volume of cone is $\frac{1}{3} \cdot \pi \cdot {r}^{2} \cdot h$ where r is radius and h is height.

Cup A:

Given $r = 13$ and $h = 32$.

Volume of cup A is $\frac{1}{3} \cdot \pi \cdot {13}^{2} \cdot 32 =$ $5663.24 C {m}^{3}$

Cup B:

Given $r = 11$ and $h = 21$.

Volume of cup B is $\frac{1}{3} \cdot \pi \cdot {11}^{2} \cdot 21 =$ $2660.91 C {m}^{3}$

As volume of cup B is less than cup A, when the full contents of cup B are poured into cup A, it will not overflow.

The filled portion in cup A is also in the form of a cone. To determine how high it is, assume height=h and radius = 13 for the filled cone part.

Volume = $\frac{1}{3} \cdot \pi \cdot {13}^{2} \cdot h$ = $2660.91 C {m}^{3}$

$h = \frac{2660.91}{\frac{1}{3} \cdot {13}^{2} \cdot \pi} = 15.0355 C m$