Question

A cylindrical tank with radius 5 m is being filled with water at a rate of 3 cubic meters per minute. How fast is the height of the water increasing

Answer 1

Explanation:

Let's calculate the volume of the tank per each meter in height.

The volume of a cylinder is πr²h, where h is the height.

A height of 1 meter in a tank with a radius of 5 meters would hold a volume of:

Vol = (3.14)*(5 meters)^2 *(1 meter)

Vol (m^3) = 78.54 m^3 per 1 meter height.

If the tank were filled at a rate of 3 m^3/min, it would rise at at a rate of:

(78.54 m^3/meter)/(3 m^3/min) = 0.0382 meters/minute [38.2 cm/min