Question:
The percentage error in the calculated volume of a sphere, if there is \(2%\) error in its diameter measurement, is _____.
The percentage error in the calculated volume of a sphere, if there is \(2%\) error in its diameter measurement, is _____.
Updated On: Apr 12, 2026
- \(1\)
- \(2\)
- \(6\)
- \(8\)
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The Correct Option is C
Solution and Explanation
Concept:
Volume of a sphere:
\[
V=\frac{4}{3}\pi r^3
\]
Since diameter \(d=2r\),
\[
V\propto d^3
\]
For small errors:
\[
\frac{\Delta V}{V}=3\frac{\Delta d}{d}
\]
Step 1: {Substitute the percentage error.}
Given error in diameter:
\[
\frac{\Delta d}{d}=2%
\]
Thus
\[
\frac{\Delta V}{V}=3\times2%
\]
\[
=6%
\]
Step 2: {Interpret the result.}
Thus the percentage error in the calculated volume is
\[
6%
\]
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