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Q.

Error in measurement of volume of a sphere is 9%, then

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a

the error in measurement of radius is 2%

b

the error in measurement of radius is 3%

c

the error in measurement surface area is 4%

d

the error in measurement surface area is 6%

answer is B, D.

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Detailed Solution

$\begin{array}{l} ∵ V = \frac{4}{3} {πR}^{3} \\ ∴ \frac{ΔV}{V} = 3 \frac{ΔR}{R} \\ or \frac{ΔV}{V} \times 100 = \frac{ΔR}{R} \times 100 \\ or 9 % = 3 \frac{ΔR}{R} \times 100 \\ ∴ \frac{ΔR}{R} \times 100 = 3 % \\ (4) ∵ A = 4 {πR}^{3} \\ ∴ \frac{ΔA}{A} = \frac{2 ΔR}{R} \\ ∴ \frac{ΔA}{A} \times 100 = 2 \frac{ΔR}{R} \times 100 = 2 \times 3 = 6 % \end{array}$

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Error in measurement of volume of a sphere is 9%, then