The relative error in the determination of the surface area of sphere is α. Then the relative error in the determination of its volume is: (a) 3/2α (b) 2/3α (c) 5/2α (d) α

Answer: (a). S = 4π r² ⇒ (Δ S)/(S) = 2(Δ r)/(r) = α, so (Δ r)/(r) = (α)/(2) V = 4/3π r³ ⇒ (Δ V)/(V) = 3(Δ r)/(r) = 3/2α So the answer is (a) 3/2α.

The relative error in the determination of the surface area of sphere… | JEE Main 2018 (15 Apr, Shift 1)

Q97JEE Main 2018 · 15 APR · SHIFT 1Easy

Errors in Measurement

The relative error in the determination of the surface area of sphere is $\alpha$ . Then the relative error in the determination of its volume is:

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Answer: (a)

$S = 4\pi r^2 \Rightarrow \frac{\Delta S}{S} = 2\frac{\Delta r}{r} = \alpha$ , so $\frac{\Delta r}{r} = \frac{\alpha}{2}$
$V = \frac{4}{3}\pi r^3 \Rightarrow \frac{\Delta V}{V} = 3\frac{\Delta r}{r} = \frac{3}{2}\alpha$
So the answer is (a) $\frac{3}{2}\alpha$ .