What is the rate of change of the surface area of the water when the water is 0.

Question

What is the rate of change of the surface area of the water when the water is 0.5 m deep? Determine an equation for the surface area of the water given the graph to the right. A trough is shaped like a half cylinder with length 5 m and radius 1 m. The trough is full of water when a valve is opened and water flows out of the bottom of the trough at a rate of 6.5m3/hr. (Hint: The area of a sector of a circle of radius r subtended by an angle alpha is r2 alpha / 1.) Complete parts (a) and (b) below. How fast is the water level changing when the water level is 0.5 m from the bottom of the trough? dh / dt = m / hr (Type an exact answer using radicals as needed.)

Explanation / Answer

flow velocity =(2gh) =(2*9.8*0.5) =3.13m/s =11268 m/hr

outflow is 6.5m^3/hr

hence hence area =6.5/11268 =0.0005768m^2

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