Volume Rate Problem: Find Change When r=6 & 24 Inches

[KatieLynn]

Homework Statement

The radius r of a sphere is increasing at a rate of 2 inches per minute. Find the rate of chance of the volume when r=6 and r=24 inches.

Homework Equations

V=(4/3)(pi)(r^3)

The Attempt at a Solution

This is what I did, I would appreciate it if someone could tell me if it is correct.

So the volume of a sphere is V=(4/3)(pi)(r^3)

So the first thing I did was derive the equation and got this...

(dv/dt)=(4/3)(3)(pi)(r^2)(dr/dt)

Simplifying it and plugging in 2 for (dr/dt) i got...

(dv/dt)=(8)(pi)(r^2)

So then I just plugged in the r and got 288pi and 4680pi, I have a feeling I've done this terribly wrong though :(

 

[Pacopag]

I didn't check your numbers, but your method seems fine to me. However, you might want to get a second opinion before you go and write it in stone.

 

[uradnky]

It all looks good to me to. Except for when the radius is 24 I got 4608. Maybe you just had a typo there?

 

[KatieLynn]

yes sorry that was a typo, thanks! :)