Draining a trough A trough in the shape of a half cylinder

Chapter 3, Problem 55

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Draining a trough A trough in the shape of a half cylinder has 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 1.5 m3>hr (see figure). (Hint: The area of a sector of a circle of a radius r subtended by an angle u is r2 u>2.) a. How fast is the water level changing when the water level is 0.5 m from the bottom of the trough? b. What is the rate of change of the surface area of the water when the water is 0.5 m deep? 5 m 1 m Out_ow 1.5 m3/h

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