A cylindrical water tank is being filled at a rate of LaTeX: 10\:m^3\:10 m 3 per minute and is leaking at a rate of LaTeX: 3\:m^33 m 3 per minute. If the water level is changing at a rate of LaTeX: \frac{4}{\pi}4 π meters/minute when the height is at 6 meters. What is the radius of the tank?

1.323 m

Explanation:

Rate of filling =

Rate of leakage =

Net change in volume of water =

= Rate of change of height =

Volume of cylinder is given by

Differentiating with respect to time we get

The radius of the tank is 1.323 m.

altitude, density, pressure

air gets less dense the higher the altitude and also the air pressure is less as altitude rises.