Related rates: A weather balloon w/ r = 9m springs a leak...

[wajiha]

A weather balloon with radius 9 meters springs a leak, losing air at 171 (pi) m^3/min. Find the rate of decrease of the radius after 4 minites.

I understand that we are given the dv/dt (= -171). I used the formula for the volume of a sphere. But I don't understand how to find the answer after 4 minutes.

 

[galactus]

\(\displaystyle \L\\\frac{dV}{dt}=4{\pi}r^{2}\frac{dr}{dt}\)

 

[wajiha]

i got that but dunno wut to do after that

 

[wjm11]

a weather balloon with radius 9 m springs a leak, losing air at 171 (pi) m^3/min. Find the rate of decrease of the radius after 4 min. i understand we are given the dv/dt, and i used the volume of the sphere formula, but i dont understand how to find the answer after 4 minutes.

You know the rate of volume loss. Simply multiply that rate times “time” (4 minutes) to calculate the lost volume. Subtract that volume from the original volume. Calculate the new radius. Plug that radius into the equation Galactus gave you.

 

[wajiha]

thanx