Mathematics

Problem

A right circular cylinder has volume

V=\pi r^{2}h

, where

r

is its radius and

h

its height, both measured in centimeters. At a certain instant the radius is 10 cm and increasing at 0.3 cm/min, while the height is 25 cm and decreasing at 0.5 cm/min. Which of the following statements about

\displaystyle\tfrac{dV}{dt}

at that instant is correct? a)

25\pi\text{ cm}^{3}\!/\text{min}

0

100\pi\text{ cm}^{3}\!/\text{min}

-50\pi\text{ cm}^{3}\!/\text{min}

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