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Q.

The radius of a sphere is measured as( $10 \pm 0.04 %$ ). The error in the measurement of its volume is

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a

5.02 cc

b

50. 2 cc

c

0.502cc

d

251. 2 cc

answer is A.

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Detailed Solution

$\begin{array}{l} V = \frac{4}{3} {πr}^{3} \frac{ΔV}{V} \times 100 = 3 \frac{Δr}{r} \times 100 \\ ΔV = \frac{4}{3} {πR}^{3} \times 3 \times \frac{Δr}{r} = \frac{4}{3} \times \frac{22}{7} \times (10)^{3} \times 3 \times \frac{0 .04}{100} = 4 \times 3 .14 \times 0 .4 = 5 .02 cc \end{array}$

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The radius of a sphere is measured as(10±0.04% ). The error in the measurement of its volume is