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

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

Answer Details

Area = $\pi r^2=\pi \times 5\times 5=25\pi$
Area error = $\pi \times {0.1}^2=0.01\pi$
$\therefore$ % error = $\frac{0.01\pi }{25\pi }\times 10$
$=\frac{0.01}{25}\times 100=\frac{1}{25}$