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Math Help - Rates of Change

  1. #1
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    Rates of Change

    A conical reservoir has a depth of 24 feet and a circular top of radius 12 feet. It is being filled so that the depth of water is increasing at a constant rate of 4 feet per hour. Determine the rate in cubic feet per hour at which water is entering the reservoir when the depth is 5 feet.

    I'm still knew to the whole finding rates of change thing but I know I'm suppose to find the derivative of the Volume, but I don't know how to deal with the equation afterward. Help?
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  2. #2
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    Quote Originally Posted by ment2byours View Post
    A conical reservoir has a depth of 24 feet and a circular top of radius 12 feet. It is being filled so that the depth of water is increasing at a constant rate of 4 feet per hour. Determine the rate in cubic feet per hour at which water is entering the reservoir when the depth is 5 feet.

    I'm still knew to the whole finding rates of change thing but I know I'm suppose to find the derivative of the Volume, but I don't know how to deal with the equation afterward. Help?

    dh/dt=4 , the question wants dv/dt when h=5

    dv/dt=dv/dh x dh/dt , using the chain rule .

    V=pir^2h
    From here , we can find dv/dh

    Now , we hv got everything , just sub into the above equation .
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  3. #3
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    what happens to dr/dt?
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  4. #4
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    Quote Originally Posted by ment2byours View Post
    what happens to dr/dt?

    It isn't required . dh/dt is given in the question but not dr/dt
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