Related Rate for Calculus 1

Question

Water is flowing into a vertical cylindrical tank of radius 3 meters at the rate of 18 cubic meters per minute. How fast is the water level rising?

Answer 1

18 cubic meters per minute flowing into a cylindrical tank of radius 3 meters.

tank's bottom's area = 9pi m^2

water level rises at the rate of 18/9pi = 2/pi per minute

= about 0.637 meters per minute

volume = bottom area times height V=Ah = 9pih, h=V/9pi

in one minute the height of the water = V/9pi = 18/9pi = 2/pi = about .637 meters