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Math Help - Volume problems/ Integration

  1. #1
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    Volume problems/ Integration

    An oil tank in the shape of a sphere has a diameter of 60ft. How much oil does the tank contain if the depth of the oil is 25 ft?

    x^2 + y^2 = 30
    25x = depth

    \pi \int_{0}^{30} (\sqrt{30 - x^2})^2 dx

    help
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  2. #2
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    An oil tank in the shape of a sphere has a diameter of 60ft. How much oil does the tank contain if the depth of the oil is 25 ft?

    x^2 + y^2 = 30
    25x = depth

    \pi \int_{0}^{30} (\sqrt{30 - x^2})^2 dx

    help
    If the diameter is 60ft, then the radius is 30ft, so the equation of the circle, if (0,0) is the origin, is
    x^2 +y^2 = 30^2
    x^2 +y^2 = 900 ------------(i)

    dV is a disc of radius x, and height dy.
    dV = pi(x^2)*dy
    dV = pi(900 -y^2)dy

    dy goes from y = -30 to y = -5

    So,
    V = (pi)INT.(-30 to -5)[900 -y^2]dy

    V = 42,542.4 cu.ft. -------------answer.
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