Water is flowing into a vertical cylindrical tank or radius 2 meters at a rate of 8 cu. meters per minute. How fast is the water level rising?

Answer 1

The Volume for Cylinder has a formula of:

V =π r ² h

Given:

r = 2 meters

dV/dt = 8 m³/ min.

First:

V = π (2) ² h

V = 4 π h

Get the derivative of both sides with respect to time (t):

dV/dt = 4 π (dh/dt)

Substitute:

8 = 4 π (dh/dt)

8/(4 π)=dh/dt

dh/dt ≈ 0.64 meters/min.