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Calculus II

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A cone-shaped water reservoir is 20 ft. in diameter and 20 ft. deep. If the reservoir is filled to a depth of 10ft., then write the integral which represents the amount of work required to pump all the water to the TOP of the reservoir.

  • Calculus II - ,

    The work required is proportional to the height, measured from the bottom.

    This integral is S (pi*R(H)^2)*(density)*g H dH. S denotes the integral sign

    The cone radius as a function of height is R(H) = H/2

    Integrate from H = 0 to h = 20 ft

    In these British units, (density* g = 62.4 lb/ft^3. The answer will be in ft-lb

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