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Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 days ago

I keep getting C when the answer is B...calc ab problem?

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    Find the volume of the cylinder of radius 2 and height 8

    pi * 2^2 * 8 =>

    32 * pi

    Now remove the solid of revolution formed by y = x^3 , x = 2 and the x-axis

    y = x^3

    y^(1/3) = x

    pi * f(y)^2 * dy , y = 0 , y = 8

    Integrate

    pi * int(y^(2/3) * dy , y = 0 , y = 8)

    pi * (1/(1 + 2/3)) * y^(2/3 + 1) + C =>

    pi * (1/(5/3)) * y^(5/3) + C =>

    (3pi / 5) * y^(5/3) + C

    (3pi/5) * (8^(5/3) - 0^(5/3)) =>

    (3pi/5) * (32 - 0) =>

    (3pi/5) * 32 =>

    (3/5) * 32 * pi

    32 * pi - 32 * pi * (3/5) =>

    32 * pi * (1 - 3/5) =>

    32 * pi * (2/5) =>

    64 * pi / 5

    What you keep finding is the solid bound by x = -2 , x = 2 and y = 8.  We're removing that from a cylinder (kind of scooping it out, as it were) and taking the remaining bit.

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  • ?
    Lv 7
    2 days ago

    See below for work and answer.

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