# Cups A and B are cone shaped and have heights of 38 cm and 24 cm and openings with radii of 12 cm and 18 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?

Jul 29, 2018

Below

#### Explanation:

Cup A
$V o l u m e = \frac{1}{3} \pi {r}^{2} h$
$V = \frac{1}{3} \pi {\left(12\right)}^{2} \left(38\right)$
$V = 1824 \pi$

Cup B
$V o l u m e = \frac{1}{3} \pi {r}^{2} h$
$V = \frac{1}{3} \pi {\left(18\right)}^{2} \left(24\right)$
$V = 2592 \pi$

Therefore, since the volume of Cup A is less than the volume of Cup B, then Cup A will overflow.