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AP® Calculus AB-BC

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Difficult

Volume Of A Cone

APCALC-BZO21I

Water is dripping from an inverted cone with a diameter of $12 \, \text{cm}$ and a height of $12 \,\text{cm}$ at a rate of $1\,\text{cm}^3/\text{min}$. At what rate is the water level decreasing when $r=2 \,\text{cm}$?

A

$3\pi \cfrac {\text{cm}} {\text {sec}} $

B

$\cfrac {1}{4\pi} \cfrac {\text{cm}} {\text {sec}}$

C

$\cfrac {1}{16\pi} \cfrac {\text{cm}} {\text {sec}}$

D

$\cfrac {3}{4\pi} \cfrac {\text{cm}} {\text {sec}}$