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water is poured into a conical paper cup so that the height increases at the constant rate of 1 inch per second. if the cup is 6 inches tall and its top has a radius of 2 inches, how fast is the volume of water in the cup increasing when the height is 3 inches?

  • calculus -

    Make a diagram, and label the radius of the water level r, and the height of the water h

    V = (1/3)πr^2h
    but by ratios, r/h = 2/6 = 1/3
    then r= h/3
    V = (1/3)π(h^2/9)(h) = (π/27)h^3
    dV/dt = (π/9)h^2 dh/dt
    = (π/9)(3^2) (1) = π cubic inches/sec

    check my arithmetic

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