# Cups A and B are cone shaped and have heights of 32 cm and 33 cm and openings with radii of 16 cm and 17 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?

Dec 24, 2016

Cone B has a greater volume than cone A, so if its contents are all poured into A, it will overflow.

#### Explanation:

Volume of cone A$= \frac{1}{3} \pi {r}^{2} h$
A$= \frac{1}{3} \pi \cdot {16}^{2} \cdot 32$
$= \frac{1}{3} \cdot 3.141592654 \cdot 256 \cdot 32$
$= \frac{1}{3} \cdot 25735.927$
$= \frac{25735.927}{3}$
Vol. A$= 8578.642 c {m}^{3}$

Vol. B$= \frac{1}{3} \pi \cdot {17}^{2} \cdot 33$
$= \frac{1}{3} \cdot 3.14159254 \cdot 289 \cdot 33$
$= \frac{1}{3} \cdot 29961.369$
$= \frac{29961.369}{3}$
Vol. B$= 9987.123 c {m}^{3}$

Cone B has a greater volume than cone A, so if its contents are all poured into A, it will overflow.

$9987.123 c {m}^{3} - 8578.642 c {m}^{3} = 1408.481 c {m}^{3}$ will be left in B if A is filled from the contents of B.