Math(Please help)
posted by Hannah .
Related Rates:
Gas is escaping from a spherical balloon at the rate of 2ft^3/min. How fast is the surface area shrinking (ds/dt) when the radius is 12ft? (A sphere of radius r has volume v=4/3 pi r^3 and surface area S=4pi r^2.)
Remember that ds/dt = ds/dr X dr/dt
Step 1: Find ds/dr
I have no clue where to start. I was going to set 2 equal to 4 pi r^2 and then take the derivative but I really have no idea.
Step 2: Find dr/dr. (HInt dv/dt= dv/dr X dr/dt
Would I set 2 equal to volume and then take derivative?
Step 3: Find ds/dt?
Step 4: Evaluate ds/dt when the radius is 12ft.
After I find my equation I would just plug in 12 correct?

Math(Please help) 
agrin04
S = 4pi*r^2
dS/dr = 4pi*2r = 8pi*r
V = (4/3)pi*r^3
dV/dr = 4pi*r^2
dV/dt = dV/dr * dr/dt
2 = 4pi*r^2 * dr/dt
dr/dt = 1/(2pi*r^2)
dS/dt = dS/dr * dr/dt
= 8pi*r * 1/(2pi*r^2)
= 4/r
If r = 12, just plug the value to the last equation 
Math(Please help) 
Hannah
How did you get 12?

Math(Please help) 
Hannah
Nevermind I meant how did you get 4/r but I figured it out. Thank You!!

Math(Please help) 
Hannah
Is this correct for the last part?
(8)(3.14)(12) X (1/(2)(3.14)(12^2) = 4/12 
Math(Please help) 
agrin04
Yes

Math(Please help) 
Hannah
Ok do I actually have to do the calculations though?

Math(Please help) 
agrin04
If you are not given the value, that means you have to write the steps I told you until the very last equation.
If you are given the value (of r), you don't have to put the value in every equation. Just follow my steps until the last equation, then plug the value after that. It's easier that way. 
Math(Please help) 
Hannah
OK thank you!

Math(Please help) 
Renz
Simplify the answer (4/12) into 1/3
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