A cylindrical tank with radius 8 meters is being filled with water at a rate of 5 cubic meters per minute. How fast is the height of the water increasing?

Question

Rate of height increasing: _________ meters per minute

Answer 1

Let's start with given:

r = 8 meters

dv/dt = 5 m³/min.

and we are looking for the rate of the height of the water increasing (dh/dt).

The formula for the volume of cylinder:

V = π r²h

plugin the value of r:

V = π 8² h

V = 64π h

Derive both sides of the equation with respect to time (t):

dV/dt = 64π • dh/dt

5 = 64π • dh/dt

dh/dt = 5 / (64π)

dh/dt ≈ 0.025 meters/min.