Calculus Related Rates Interesting Problem

[Gregarious101]

Homework Statement

http://www.kent.k12.wa.us/pcpow/questions/calc/0401trickortreat/index.html

This is an old problem, and I have been able to solve one and two, I believe the answers are

1. pi cm/second
2. 50(pi) cm^3/second
3. This is the one I am not sure of. How can I solve this? Isn't there two many variables?

Homework Equations

V=4/3(pi)r^3
dV/dt= 2(pi)r^2
dC/dt= (2(pi))*cube root(V/(4/3(pi)))*(1/(4/3(pi)))*(dV/dt)

The Attempt at a Solution

I am getting lost at three, the rest are pretty easy, I think.

THANK YOU!

 

[tiny-tim]

Welcome to PF!

Hi Gregarious101! Welcome to PF!

(have a pi: π and try using the X² tag just above the Reply box )

I am getting lost at three, the rest are pretty easy, I think.

3. The balloons are all full now and the kids are ready to go. A little boy named Billy grabs a water balloon but realizes the he’s already getting wet even though no balloon has been tossed. Billy looks down at his balloon.
OH NO! There is a small leak in his balloon. The circumference is decreasing at a rate of 1/8 cm per second.
If the balloon is empty after five minutes, what was the volume of the balloon before it began to leak (round to three decimal places)?

Just do it the other way …

The circumference is increasing at a rate of 1/8 cm per second: if it starts empty, what its it after five minutes?