Acylider of radius x is inscribed in a fixed sphere of internal radius R, the circumference of the circular ends of the cylider being in contact with the inner surface of the sphere.

a) Show that A^2=16pi^2x^2(R^2-x^2), where A is the curved surface area of the cylider.

b) Prove that, if x is made to vary, the maximum value of is obtained when the height of the cylinder is equal to the diameter.

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Prove the maximum value of is obtained : Acylider of radius x is inscribed in a fixed sphere of internal radius R, the circumference of the circular ends of the cylider being in contact with the inner surface of the sphere. |

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