Question

The error in the measurement of the radius of a sphere is $0.5$ %. Find the permissible error in the measurement of surface area?

• A. $0.1$ %
• B. $10$ %
• C. $5$ %
• D. $1$ %

Answer 1

The correct option is D $1$ %

The percentage error in measurement of radius is given, $\frac{\Delta r}{r}\times 100=0.5$%
Thus, $\frac{\Delta r}{r}=0.5/100=0.005$
The surface area of sphere is $S=4\pi r^2$
Take ln and differentiate, $\frac{\Delta S}{S}=2\frac{\Delta r}{r}=2\times 0.005=0.01$
The permissible or % error in the measurement of surface area $=\frac{\Delta S}{S}\times 100=0.01\times 100=1$%