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Math Help - cylinder in a sphere

  1. #1
    Senior Member furor celtica's Avatar
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    cylinder in a sphere

    a cylinder is cut from a solid sphere of radius 3cm. given that the cylinder has height 2h, find its radius in terms of h. hence show that the volume V cubic centimetres of the cylinder is given by
    V = 2 x pi x h (9 - h^2)
    now this has me stuck bcos i would have tried to find a relation between r and h by using the formula for V. but since this is ruled out, i really have no idea where to start.
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  2. #2
    Master Of Puppets
    pickslides's Avatar
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    pretty hard to explain this one without a diagram to point at

    r = \sqrt{3^2-h^2}

    Is taken from a right angled triangle where the long side (3 units) is from the middle to the point where the top of the cylinder meets the sphere. The 2 shorter sides are half of the height of the cylinder (h) and the remaining small side is the radius of the sphere.
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  3. #3
    Senior Member furor celtica's Avatar
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    thanks i have a diagram but i didnt feel the need to attach it, i'll figure it out with what you said.
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