Can you help me see the steps to doing this problem Thank yo

Can you help me see the steps to doing this problem?

Thank you!

Water is draining at a rate of 2 cubic feet per minute from the bottom of a conically shaped storage tank of overall height 6 feet and radius 2 feet (see sketch below). How fast is the height of water in the tank changing when 8 cubic feet of water remain in the tank? Include appropriate units in your answer. (Note: The volume of a cone is given by V = 1/3 pi r2 h.) Your answer may be expressed in terms of n .

Solution

h = 4r r = h/4 V = 1/3 p r² h V = 1/3 p (h/4)² h V = 1/48 p h³ Differentiate both sides with respect to t: dV/dt = 1/16 p h² dh/dt Now we find dh/dt when dV/dt = -2, h = 6 -2 = 1/16 p (6)² dh/dt dh/dt = -2.7925 Depth is decreasing at rate of 2.7995 ft/min