Physics

# 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$\pi r^2$) $\dfrac{\Delta A}{A}=\dfrac{2\Delta r}{r})$

##### SOLUTION
Given, Error in a radius of the sphere is 2%
it means$\Delta r=2%$
Now, the surface area of the sphere is
$A=4\pi r^2$
$\dfrac{\Delta A}{A}$=$\dfrac{2\Delta r}{r}$
$\dfrac{\Delta A}{A}$=$\dfrac{2\times 2}{1000}$=$0.04$
$\dfrac{\Delta A}{A\times 100}$=$0.04\times 100$= 4%
it means % error in surface area of its measurements is 4%

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