The water tank in the diagram below is in the shape of an inverted right circular cone. The radius of its base is 16 feet, and its height is 120 feet. The water in the tank is 25% of the tank's capacity. What is the height of the water?
+129899 Total capacity = pi * r^2 * h / 3 = pi * (16)^2 * 120 / 3 = 10240 pi ft^3
.25 capacity = 2560 pi
Using similar triangles we have that r / h = 16 /120 = 2 /15 so r = 2h /15
So
2560 pi = pi ( 2h/15)^2 * h simplify
2560 = (4/225)h^3
2560 (225/4) = h^3
144000 = h^3 take the cube root of both sides
h ≈ 52.4 ft when 25% of capacity
