A hemispherical bowl contains water of depth h cm. The vol of water is given by 1/3πh^2(18-h)cm^3. Water is poured into the bowl at a rate of 3cm3s-1. Find rate of increase of water level depth=3cm.

Question

Any help would be appreciated. Thank you in advance.

Answer 1

The volume formula that's given is V = .5πh²(18-h), the volume's rate of change is dV/dt = 3cm³/sec, and you're finding the rate of increase of the water level (dh/dt) at h = 3cm.

The first thing you can do is take the derivative of the left and right side of the volume formula with respect to time. Once that's done you'll input all known values leaving one unknown (dh/dt), solve for dh/dt and you'll have your solution.

Hope this sparks some ideas!