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    Question: A cylinder is cut from a solid sphere of radius 5 cm. If the height of the cylinder is 2h, show that the volume of the cylinder is  2\pi h(25-h^2)

    My initial thoughts on this, was the fact that they only gave the radius of the sphere and neglected to give the radius of cylinder. I'm guessing there is some type of relationship between the radius of the sphere and cylinder that I'm expected to know, that I don't know currently.

    Any thoughts?
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    (Original post by MathQS)
    Question: A cylinder is cut from a solid sphere of radius 5 cm. If the height of the cylinder is 2h, show that the volume of the cylinder is  2\pi h(25-h^2)

    My initial thoughts on this, was the fact that they only gave the radius of the sphere and neglected to give the radius of cylinder. I'm guessing there is some type of relationship between the radius of the sphere and cylinder that I'm expected to know, that I don't know currently.

    Any thoughts?
    Well you can work out the radius of the cylinder from the final form they give you, this should give you a hint of how they got that in the first place.
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    (Original post by MathQS)
    Question: A cylinder is cut from a solid sphere of radius 5 cm. If the height of the cylinder is 2h, show that the volume of the cylinder is  2\pi h(25-h^2)

    My initial thoughts on this, was the fact that they only gave the radius of the sphere and neglected to give the radius of cylinder. I'm guessing there is some type of relationship between the radius of the sphere and cylinder that I'm expected to know, that I don't know currently.

    Any thoughts?
    Just imagine a sphere of radius 5. Inscribe a cylinder into it so that it looks like this (ignore the measurement of h here):

    Spoiler:
    Show







    The sphere and the cylinder share the same center. We know the radius of the sphere is 5, therefore the distance from the centre of the cylinder to one of the corners is 5 and hence you can start labelling some more:

    Spoiler:
    Show






    By considering the right-angled triangle I'd indicated, you can work out the radius of the cylinder in terms of h.
 
 
 
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