5. (10 marks] Suppose R — r0 gt; 0 and we assume both r0 andR are positive. We remove a central cylinder of radius r0 from a sphere of radius R. Show, W that the resulting volume of the remaining portion of sphere is k[(R + T0)(R — r0)]2 , where k is a constant. Show the value of the constant k

explictly in your ﬁnal answer. (Hint: Without loss of generality, we may simply assume that the sphere is centered at the origin.)

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