Question

If the error committed in measuring the radius of the circle is $0.05\%$, then the corresponding error in calculating the area is:

• A. $0.05\%$
• B. $0.025\%$
• C. $0.25\%$
• D. $0.1\%$

Answer 1

The correct option is D $0.1\%$

$\frac{dr}{r}=0.05\Rightarrow dr=\left(0.05\right)r$

Area of circle $=\pi r^2$

$A=\pi r^2\Rightarrow \frac{dA}{dr}=2\pi rdA=2\pi rdr\Rightarrow \frac{dA}{A}=\frac{2\pi rdr}{\pi r^2}=\frac{2dr}{r}\therefore \frac{dA}{A}=2(0.05{)}^2=0.1$

$\therefore$ Corresponding error in area $=0.1\%$