Question

Oil pours into a conical tank at the rate of 27 cubic inches per minute. The tank stands point down and has a height of 10 inches and a base radius of 9 inches. How fast is the oil level rising when the oil is 6 inches deep? inches per minute Round your answer to four decimal places.

Answer 1

At any time R = .9 H where V = π/3 R^2 H (conical pyramid)

dV/dt = π/3 [R^2 dH/dt + 2 R H dR/dt]

dR/dt = .9 dH/dt

dV/dt = π/3 [R^2 dH/dt + 2 (.9) R H dH/dt]

dV/dt = π/3 [R^2 + 1.8 R H] dH/dt

When H = 6 R = 5.40

27 = π/3 [5.4^2 + 1.8 * 5.4 * 6] dH/dt

27 = 61.0726 dH/dt

dH/dt = .4421 in/min