A) 1%
B) 1/3%
C) 3%
D) 10%
Correct Answer: C
Solution :
Key Idea: Volume of sphere is proportional to cube of radius. Let R be the radius of a sphere. Volume of sphere \[=\frac{4}{3}\pi {{R}^{3}}\] Taking log on both sides, we have \[\log \,V=log\frac{4}{3}\pi +\log \,{{R}^{3}}\] \[\log \,V=\log \frac{4}{3}\pi +3\log R\] In order to obtain change in volume, we differentiate both sides. \[\therefore \] \[\frac{\Delta V}{V}=\frac{3\Delta R}{R}\] \[\therefore \] Percentage change in volume \[=3\times \] percentage change in radius\[=3\times 1%=3%\]
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