The radius of a sphere is increased by 10 %. | vedclass

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(A) The surface area $S$ of a sphere is given by the formula $S = 4 \pi r^2$,where $r$ is the radius.Since $4$ and $\pi$ are constants,the surface are

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$21 \%$

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(A) The surface area $S$ of a sphere is given by the formula $S = 4 \pi r^2$,where $r$ is the radius.Since $4$ and $\pi$ are constants,the surface area is directly proportional to the square of the radius $(S \propto r^2)$.When a quantity changes by $x \%$ and then by $y \%$,the net percentage change is given by the formula $\left(x + y + \frac{xy}{100}ight) \%$.Here,the radius increases by $10 \%$,so $x = 10$ and $y = 10$.Substituting these values into the formula:Net $\%$ change $= \left(10 + 10 + \frac{10 	imes 10}{100}ight) \% = (20 + 1) \% = 21 \%$.

The radius of a sphere is increased by $10 \%$. The surface area increases by

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