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Question
A sphere is made of ice having radius 10 cm. Its radius decreases from 10 cm to 9.8 cm. Find approximations for the following:
Change in the surface area
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Solution
Surface area of the sphere
S(r) = 4πr2
S'(r) = 8πr
Change in surface area at r = 10 is
= S'(r)[10 – 9.8]
= 8π (10)(0.2)
= 16π cm2
∴ Surface Area decreases by 16π cm2
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