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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Definitions:

Double Taxation

A taxation principle referring to income taxes paid twice on the same source of earned income, often seen in international business or when corporate income is taxed both at the corporate and personal levels.

Preferred Stock

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