Posted by **Hannah** on Friday, March 4, 2011 at 10:31pm.

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**, Friday, March 4, 2011 at 11:46pm
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**, Saturday, March 5, 2011 at 12:52am
How did you get 12?

- Math(Please help) -
**Hannah**, Saturday, March 5, 2011 at 12:57am
Nevermind I meant how did you get 4/r but I figured it out. Thank You!!

- Math(Please help) -
**Hannah**, Saturday, March 5, 2011 at 1:53am
Is this correct for the last part?

(8)(3.14)(12) X (1/(2)(3.14)(12^2) = 4/12

- Math(Please help) -
**agrin04**, Saturday, March 5, 2011 at 2:14am
Yes

- Math(Please help) -
**Hannah**, Saturday, March 5, 2011 at 2:23am
Ok do I actually have to do the calculations though?

- Math(Please help) -
**agrin04**, Saturday, March 5, 2011 at 6:40am
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**, Saturday, March 5, 2011 at 10:55am
OK thank you!

- Math(Please help) -
**Renz**, Sunday, October 9, 2016 at 8:44pm
Simplify the answer (4/12) into 1/3

## Answer This Question

## Related Questions

- Math(Please check) - I posted this question a few days ago and someone answered ...
- math - Example: 1 Gas is escaping from a spherical balloon at the rate of 2 ft3...
- calculas - i didnot under stand the question ? need help Gas is escaping a ...
- Calculus - Gas is escaping a round balloon at2units^2/min.How fast is the ...
- Calculus - A spherical balloon is being inflated and the radius of the balloon ...
- calc rates - Air is being pumped into a spherical balloon so that its volume ...
- calculus - a spherical balloon filled with gas has a leak that permits the gas ...
- Math - A spherical balloon expands uniformly as it is inflated. The radius of ...
- Calculus Related Rates - If a spherical balloon is inflated and its volume is ...
- Calc - Air is being pumped into a spherical balloon so that its volume increases...

More Related Questions