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). The area of a sector of a circle of a radius r subtended by an angle θ is r² θ/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?

Transcribed Image Text:

5 m Outflow 1.5 m³/h