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) $\frac { d V } { d t } = 3 r ^ { 2 } \frac { d r } { d t }$

Question

Quizplus · Accepted Answer

We use the formula for the volume of a sphere, differentiate both sides with respect to time and apply the chain rule:
$$\frac { dV } { dt } = \frac { d } { dt } \left( \frac { 4 } { 3 } \pi r ^ { 3 } \right) = 4 \pi r ^ { 2 } \frac { d r } { d t }$$

Solve the Problem rrr And Volume V=43πr3\mathrm { V } = \frac { 4 } { 3 } \pi \mathrm { r } ^ { 3 }V=34​πr3

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