Question

A spherical balloon is inflated with gas at a rate of 600 cubic centimeters per minute. (a) Find the rates of change of the radius when r = 30 centimeters and r = 45 centimeters. r = 30 $ Correct: Your answer is correct. cm/min r = 45 $ Correct: Your answer is correct. cm/min (b) Explain why the rate of change of the radius of the sphere is not constant even though dV/dt is constant.

Answer 1

Answer:

Given,

$\frac{d v}{d t}=600 cubic centimeters/min.$

We know that,

$V=\frac{4}{3} \pi r^{3}$

$\frac{d v}{d t}=4 \pi r^{2} \frac{d r}{d t}\\\Rightarrow \quad 600=4 \pi \gamma^{2} \frac{d \gamma}{d t}$

$\frac{dr}{dt}=\frac{150}{\pi r^{2} }$

Which contains variable,

So, $\frac{dr}{dt}$ is not constant.