# Application of derivative: a SPHERICAL balloon filled w gas has a leak that cause gas to escape at rate of 1.5m^3/min.?

At what rate is surface area shrinking when radius is 4m¿

### 1 Answer

Relevance

- oldschoolLv 73 months agoFavorite Answer
V = (4/3)πr³

S = 4πr²

We need to find the rate of the radius shrinking because

dV/dt = dV/dr * dr/dt = 4πr² * dr/dt = -1.5m³/min

dr/dt = -1.5/4πr²

ds/dt = ds/dr * dr/dt = -8πr * 1.5/4πr² = -3/r m²/s

-3/4 = -0.75m²/min

-0.75m²/60s * (100cm/1m)²= -125cm²/s <<<<<

- Login to reply the answers

Still have questions? Get your answers by asking now.