Error in measurement of radius of a sphere is 1%, then

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the error in measurement in volume is 1%

the error in measurement of surface area is 2%

the error in measurement of volume is 3%

the error in measurement of surface area is 6%

answer is A, C.

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Detailed Solution

$\begin{array}{l} ∵ V = \frac{4}{3} {πR}^{3} \\ ∴ \frac{ΔV}{V} = \frac{3 ΔR}{R} \\ ∴ \frac{ΔV}{V} \times 100 = 3 \frac{ΔR}{R} \times 100 = 3 % \\ (3) A = 4 {πR}^{2} \\ ∴ \frac{ΔA}{A} = \frac{2 ΔR}{R} \\ ∴ \frac{ΔA}{A} \times 100 = 2 (\frac{ΔR}{R} \times 100) = 2 \times 1 % = 2 % \end{array}$

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