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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