Mathematics in Physics

JEE Main level, single correct, medium

103 of 121

Question 103 of 121

The diameter and height of a cylinder are measured by a meter scale to be 12.6±0.1cm12.6\pm 0.1 cm and 34.2±0.1cm34.2\pm 0.1 cm , respectively. What will be the value of its volume in appropriate significant figures?

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Answer: (C) 4260±80cm34260\pm 80c{m}^{3}

V=πd2h4=π4(12.6)2(34.2)cm3V=\dfrac{\pi {d}^{2}h}{4}=\dfrac{\pi }{4}{\left(12.6\right)}^{2}\left(34.2\right)c{m}^{3}

dVV=2d(d)d+d(h)h\dfrac{dV}{V}=\dfrac{2d\left(d\right)}{d}+\dfrac{d\left(h\right)}{h}

Converting to errors

∆VV=2∆dd+∆hh\dfrac{∆V}{V}=2\dfrac{∆d}{d}+\dfrac{∆h}{h}

∆V4260=2(0.112.6)+(0.134.2)\dfrac{∆V}{4260}=2\left(\dfrac{0.1}{12.6}\right)+\left(\dfrac{0.1}{34.2}\right)

⇒∆V=80cm3\Rightarrow ∆V=80c{m}^{3}

V=4260±80cm3V=4260\pm 80c{m}^{3}

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