Question:
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 :
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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Surface area \(\propto r^2\) and volume \(\propto r^3\); relative error of \(r^n\) is \(n\) times the relative error of \(r\).
Updated On: Nov 11, 2026
- \(\frac32\alpha\)
- \(\frac23\alpha\)
- \(\frac52\alpha\)
- \(\alpha\)
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The Correct Option is A
Solution and Explanation
Surface area \(S=4\pi r^2\), so \(\frac{\Delta S}{S}=2\frac{\Delta r}{r}=\alpha\), giving \(\frac{\Delta r}{r}=\frac\alpha2\).
Volume \(V=\frac43\pi r^3\), so \(\frac{\Delta V}{V}=3\frac{\Delta r}{r}=3\cdot\frac\alpha2=\frac32\alpha\).
Answer: (1) \(\frac32\alpha\)
Volume \(V=\frac43\pi r^3\), so \(\frac{\Delta V}{V}=3\frac{\Delta r}{r}=3\cdot\frac\alpha2=\frac32\alpha\).
Answer: (1) \(\frac32\alpha\)
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