Question

reservoir has the shape of a right-circular cone. The altitude is 10 feet, and the radius of the base is 4 ft. Water is poured into the reservoir at a constant rate of 5 cubic feet per minute. How fast is the water level rising when the depth of the water is 5 feet?

Answer 1

since h = (10/4) r,

v = pi/3 r^2 (10/4 r)
= 5pi/6 r^3

now differentiate and solve for dr/dt