The Volume of a Right Circular Cone of Radius $r$ And Height

question 50

Essay

The volume of a right circular cone of radius $r$ and height $h$ is $V = \frac { \pi } { 3 } r ^ { 2 } h$ . Suppose that the radius and height of the cone are changing with respect to time $t$ .
a. Find a relationship between $\frac { d V } { d t } , \frac { d r } { d t }$ , and $\frac { d h } { d t }$ .
b. At a certain instant of time, the radius and height of the cone are $12 \mathrm { in }$ . and 13 in. and are increasing at the rate of $0.2 \mathrm { in } . / \mathrm { sec }$ and $0.5 \mathrm { in } . / \mathrm { sec }$ , respectively. How fast is the volume of the cone increasing?

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