Need Help

[bamby]

A spherical baloon is inflated with a gas at rate 500cm3/min. How fast is the radius of the baloon increasing at the instant the n is 30 cm?

Thanks?

 

[BigGlenntheHeavy]

$\displaystyle V_{Sphere} \ = \ \frac{4}{3} \pi r^{3}$

$\displaystyle \frac{dV}{dt} \ = \ 4\pi r^{2}\frac{dr}{dt}$

$\displaystyle Now \ \frac{dV}{dt} \ = \ 500 \ and \ when \ r \ = \ 30, \ then \ 500 \ = \ 4\pi(30^{2})\frac{dr}{dt}$

$\displaystyle Therefore, \ \frac{dr}{dt} \ = \ \frac{5}{36\pi} \ cm/min$

Note: I'm assuming that n = radius, not diameter.