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Question

A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease in its volume is
(a) 12000 π mm3
(b) 800 π mm3
(c) 80000 π mm3
(d) 120 π mm3

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Solution

(c) 80000 π mm3

Let x be the radius of the sphere and y be its volume.

x=100, x+x=98x=-2y=43πx3dydx=4πx2dydxx=100=40000π y=dy=dydxdx=40000π×-2=-80000πHence, the decrease in the volume of the sphere is 80000π mm3.

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