Question

An upright cylindrical tank with radius 5 m is being filled with water at a rate of 2 m3/min. How fast is the height of the water increasing? (Round the answer to four decimal places.)

Answer 1

The height of water increasing is 8.5 x 10^-4 m/s.

Step-by-step explanation:

radius, r = 5 m

Volume per second, dV/dt = 2 m^3/min = 2/60 m^3/s

Let the height of cylinder is h.

The volume of the cylinder is given by

`V = \pi r^2 h \\\\(dV)/(dt) = \pi r^2 (dh)/(dt)\\\\(2)/(30) = 3.14* 5* 5* (dh)/(dt)\\\\(dh)/(dt)=8.5 * 10^(-4) m/s`