Solve the Problem $r$ And Volume $\mathrm { V } = \frac { 4 } { 3 } \pi \mathrm { r } ^ { 3 }$

question 436

Multiple Choice

Solve the problem.
-Suppose that the radius $r$ and volume $\mathrm { V } = \frac { 4 } { 3 } \pi \mathrm { r } ^ { 3 }$ of a sphere are differentiable functions of $\mathrm { t }$ . Write an equation that relates $\mathrm { dV } / \mathrm { dt }$ to $\mathrm { dr } / \mathrm { dt }$ .

• A) \(\frac { d V } { d t } = 4 \pi r ^ { 2 } \frac { d r } { d t }\)
• B) \(\frac { d V } { d t } = 4 \pi \frac { d r } { d t }\)
• C) \(\frac { d V } { d t } = \frac { 4 } { 3 } \pi r ^ { 2 } \frac { d r } { d t }\)
• D) \(\frac { d V } { d t } = 3 r ^ { 2 } \frac { d r } { d t }\)

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