Question

Please help me with this question

Answer 1

Answer:

Step-by-step explanation:

Haven't seen a related rates problem in a while! These are fun!  Not too bad when you keep your stuff organized.  First, label what you've been given.  If the radius is decreasing, then we have

$\frac{dr}{dt}=-.2$

We are told to find $\frac{dV}{dt}$ when r = 9.

Now we have to find the derivative of the volume of a sphere using implicit differentiation.  The derivative is

$\frac{dV}{dt}=\frac{4}{3}\pi3r^2\frac{dr}{dt}$

It looks like we have everything we need to solve for the unknown.  The derivative is even already set up to solve for the change in volume.  All we have to do now is plug in the values.

$\frac{dV}{dt}=\frac{4}{3}\pi3(81)(-.2)$

This does give us a negative number, -203.575 to be exact, but if you answer it without the negative, you say that the volume is decreasing at the rate of 203.575 cm/min cubed