The diameter and height of a cylinder are measured by a meter scale… | JEE Main 2019 (10 Jan, Shift 2)

Q95JEE Main 2019 · 10 JAN · SHIFT 2Medium

Errors in Measurement

The diameter and height of a cylinder are measured by a meter scale to be 12.6 $\pm$ 0.1 cm and 34.2 $\pm$ 0.1 cm, respectively. What will be the value of its volume in appropriate significant figures?

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Answer: (d)

$V = \frac{\pi d^2 h}{4} = \frac{\pi (12.6)^2 (34.2)}{4} \approx 4264\text{ cm}^3$
$\frac{\Delta V}{V} = 2\frac{\Delta d}{d} + \frac{\Delta h}{h} = 2\left(\frac{0.1}{12.6}\right) + \frac{0.1}{34.2} = 0.0159 + 0.0029 = 0.0188$
$\Delta V = 0.0188 \times 4264 \approx 80\text{ cm}^3$
Data have 3 significant figures, so $V = 4260 \pm 80\text{ cm}^3$ .
So the answer is (d) $4260 \pm 80\text{ cm}^3$ .

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