Q 11-01-228JEE MainJEE Main 2018 (15 Apr, Shift 1)Easy
The relative error in the determination of the surface area of a sphere is $\alpha$. The relative error in the determination of its volume is
Answer: (A) $\dfrac{3}{2}\alpha$
Surface area $S = 4\pi r^2$, so
$$\frac{\Delta S}{S} = 2\frac{\Delta r}{r} = \alpha \quad\Rightarrow\quad \frac{\Delta r}{r} = \frac{\alpha}{2}$$
Volume $V = \dfrac43\pi r^3$, so
$$\frac{\Delta V}{V} = 3\frac{\Delta r}{r} = \frac{3}{2}\alpha$$
Solution by Sreeraj P, M.Sc Physics