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I had this on a test yesterday, and for some reason it seems like it was way too simple.

A cone with a radius of 5 ft and height of 10 ft is being filled with water at a rate of 3 ft^3/min. Find the rate at which the height of the water is changing when the height is 7 ft.

So I have V=1/3 B * H, with the base being 25 pi, and dv/dt being 3 ft^3/min.

dv/dt=1/3(25 * pi * dh/dt)

3=1/3(25 * pi * dh/dt)

9=25 * pi * dh/dt

9/(25pi)=dh/dt

dh/dt=0.1146 ft/min

Is this correct? This is what I got the first time I did the problem, but I remember writing down my answer as 1.14 ft/min because that was the answer I got the second time I did it. It seems too simple, especially because this was worth twice as many points as any other problems on the test.

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# Caclculus question

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