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If the radius of a sphere is measured...

If the radius of a sphere is measured as 9 cm with an error or 0.03 m, find the approximate error in calculating its surface area.

Text Solution

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Let r be the radius and S be the total surface area of the sphere.
Given ` r = 9 m and Delta r = 0.03 cm`
Now ` S = 4pi r^(2)`
` rArr (dS)/(dr) = 8 pi r`
`:. Delta S = (dS)/(dr) * Delta r = 8 pi r * Dleta r`
` = 8 pi xx 900 xx 0.03 cm^(2)`
` = 216 pi cm^(2)`
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