JAMB 1992 · UME · Q2

The radius of a circle is given as 5 cm subject to an error of 0.1 cm. What is the percentage error in the area of the circle?

Worked solution (try it first)

The area is $A = \pi r^2$ , so it depends on the square of the radius.
The relative error in $r$ is $\frac{0.1}{5} = 0.02$ , or 2%.
Squaring doubles a small relative error, so the error in the area is about $2 \times 2\% = 4\%$ .
Check: $\frac{\pi(5.1^2 - 5^2)}{\pi \times 5^2} = \frac{1.01}{25}$
$= 4.04\%$ , which is 4%, option C.