Q 11-01-216JEE MainJEE Main 2019 (10 Jan, Shift 2)Medium
The diameter and height of a cylinder are measured by a meter scale to be $12.6 \pm 0.1\ \text{cm}$ and $34.2 \pm 0.1\ \text{cm}$, respectively. What will be the value of its volume in appropriate significant figures?
Answer: (C) $4260 \pm 80\ \text{cm}^3$
$$V = \frac{\pi d^2h}{4} = \frac{\pi(12.6)^2(34.2)}{4} \approx 4264.4\ \text{cm}^3$$
$$\frac{\Delta V}{V} = 2\frac{\Delta d}{d} + \frac{\Delta h}{h} = \frac{0.2}{12.6} + \frac{0.1}{34.2} = 0.0188 \;\Rightarrow\; \Delta V \approx 80\ \text{cm}^3$$
The measurements have 3 significant figures, so $V = 4260 \pm 80\ \text{cm}^3$.
Solution by Sreeraj P, M.Sc Physics