Question

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

Answer 1

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

Answer 2

\[V Prime = 4\pi r^2\]

Answer 3

V Prime = rate of change of sphere

Answer 4

substitute 2 = r for radius, then evaluate

Answer 5

So the answer is 16pi

Answer 6

How did you get V prime? Find the derivative?

Answer 7

Yes

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

I'm sorry to hear that

Answer 12

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

Answer 13

Um, well....hold on

Answer 14

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

Answer 15

LOL okay.. thanks though =]