# related rates problem

• Oct 22nd 2009, 01:59 PM
jawisbest
related rates problem
The volume of a sphere is increasing at a rate of 10 cm3/sec. Find the rate of change of its surface area when its volume is 32π/3 cm3.

Using my crazy logic I ended up coming up with 20 / r... anything will help
• Oct 22nd 2009, 02:08 PM
rn443
Quote:

Originally Posted by jawisbest
The volume of a sphere is increasing at a rate of 10 cm3/sec. Find the rate of change of its surface area when its volume is 32π/3 cm3.

Using my crazy logic I ended up coming up with 20 / r... anything will help

Find the radius r when the sphere has a volume of 32pi/3. Next, V = (4pi/3)*r^3, so V' = 4pi*r^2*r' = 10. Use this and the value you found for r to find r'. Also, A = 4pi*r^2, so A' = 8pi*r*r'. Use the values you found for r and r' to find A'.
• Oct 22nd 2009, 02:37 PM
jawisbest
So did all of that and came up with 4.367... can anyone confirm this?
• Oct 22nd 2009, 03:11 PM
skeeter
Quote:

Originally Posted by jawisbest
So did all of that and came up with 4.367... can anyone confirm this?

$\displaystyle \frac{dS}{dt} \ne 4.367$