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If there is an error 0.05 sq.cm in the surface area of a sphere then the error in its volume when the radius 20 cm is

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1 c.c

0.5 c.c

2.5 c.c

1.5 c.c

answer is B.

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Detailed Solution

s= $s = 4 π r^{2} \Rightarrow δ s = 4 π (2 r) δ r \Rightarrow 0.05 = 4 π \times 40 \times δ r \Rightarrow δ r = \frac{1}{3200 π} v = \frac{4}{3} π r^{3} \Rightarrow δ v = 4 π r^{2} δ r = 1600 π \times \frac{1}{3200 π} = \frac{1}{2}$

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