Question

the error in the measurement of radius of a sphere is 2% . what will be the error oin the calculation of its surface area?

Answer 1

It is given that $\frac{∆R}{R}=0.02$

Surface area of sphere of radius (R) = $4{\mathrm{\pi R}}^2$
$\frac{∆S}{S}=2\frac{∆R}{R}=2\times 0.02=0.04$

Error in the calculation of its surface area is 0.04.
Therefore, the percentage error = 0.04 × 100 = 4%