Question

The error in the measurement of radius of a sphere is 2%. What will be the error in the calculation of its surface area?
(surface area A=4$\pi r^2$) $\frac{\Delta A}{A}=\frac{2\Delta r}{r})$

Answer 1

Given, Error in a radius of the sphere is 2%

it means$\Delta r=2$

Now, the surface area of the sphere is

$A=4\pi r^2$

$\frac{\Delta A}{A}$=$\frac{2\Delta r}{r}$

$\frac{\Delta A}{A}$=$\frac{2\times 2}{1000}$=$0.04$

$\frac{\Delta A}{A\times 100}$=$0.04\times 100$= 4%

it means % error in surface area of its measurements is 4%