What is the rate of change of the volume of a sphere with respect to the radius when the radius is r = 2 in.?

Question

hero · Answer

$$V_{sphere} = \frac{4\pi r^3}{3}$$

hero · Answer

$$V Prime = 4\pi r^2$$

hero · Answer

V Prime = rate of change of sphere

hero · Answer

substitute 2 = r for radius, then evaluate

hero · Answer

So the answer is 16pi

anonymous · Answer

How did you get V prime? Find the derivative?

hero · Answer

Yes

anonymous · Answer

Ok, so when finding the derivative, I would plug (x+h) into r?

hero · Answer

Oh you haven't learned the shortcut for taking derivative?

anonymous · Answer

No, not yet.. our teacher is making us do the definition of a derivative.

hero · Answer

I'm sorry to hear that

anonymous · Answer

Lol, it's okay, in this case I would put (x+h) into r then, right?

hero · Answer

Um, well....hold on

hero · Answer

Good luck with using definition of derivative to do this. Your teacher should have shown you how to do it by now.

anonymous · Answer

LOL okay.. thanks though =]