If the diameter of a cylinder is 12.6 ± 0.1 cm and its height is 34.2 ± 0.1 c m , then find the volume of the cylinder to the nearest significant figure.

V = πd 2 h 4 = π 4 12.6 2 34.2 cm 3 dV V = 2 d d d + d h h Converting to errors, ∆ V V = 2 ∆ d d + ∆ h h ∆ V 4260 = 2 0.1 12.6 + 0.1 34.2 ⇒ ∆ V = 80 cm 3 V = 4260 ± 80 cm 3

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Physics - Unit & Dimension Question with Solution | TestHub

PhysicsUnit & DimensionMiscellaneousEasy2 minPYQ_2020

PhysicsEasysingle choice

If the diameter of a cylinder is $12.6 \pm 0.1 cm$ and its height is $34.2 \pm 0.1 c m$ , then find the volume of the cylinder to the nearest significant figure.

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Answer:

Solution:

$V = \frac{{πd}^{2} h}{4} = \frac{π}{4} {(12.6)}^{2} (34.2) {cm}^{3}$

$\frac{dV}{V} = \frac{2 d (d)}{d} + \frac{d (h)}{h}$

Converting to errors,

$\frac{∆ V}{V} = 2 \frac{∆ d}{d} + \frac{∆ h}{h}$

$\frac{∆ V}{4260} = 2 (\frac{0.1}{12.6}) + (\frac{0.1}{34.2})$

$\Rightarrow ∆ V = 80 {cm}^{3}$

$V = 4260 \pm 80 {cm}^{3}$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:Unit & DimensionSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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