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

Correct answer: C. 4260 ± 80c m ^ 3 V = π d ^ 2 h 4 = (π)/(4) (12.6) ^ 2 (34.2)c m ^ 3 (dV)/(V) = (2d(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 = 80c m ^ 3 V = 4260 ± 80c m ^ 3

JEE Main 201910 JanuaryEvening Shift

Exam: JEE Main
Year: 2019
Date: 10 January
Shift: Evening Shift
Subject: Physics
Chapter: Mathematics in Physics

JEE Main 2019 · 10 January · Evening Shift · Physics · Mathematics in Physics

The diameter and height of a cylinder are measured by a meter scale...

The diameter and height of a cylinder are measured by a meter scale to be

12.6 \pm 0.1cm

and

34.2 \pm 0.1cm

, respectively. What will be the value of its volume in appropriate significant figures?

Options

A $4264 \pm 81c{m}^{3}$
B $4264.4 \pm 81.0c{m}^{3}$
C $4260 \pm 80c{m}^{3}$
D $4300 \pm 80c{m}^{3}$

Correct answer

C. $4260 \pm 80c{m}^{3}$

Step-by-step solution

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

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

Converting to errors

\dfrac{∆ V}{V} = 2\dfrac{∆ d}{d} + \dfrac{∆ h}{h}

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

⇒ ∆ V = 80c{m}^{3}

V = 4260 \pm 80c{m}^{3}

Practice Mathematics in Physics on Quantrex Academy →

More from Mathematics in Physics

The density ρ of a uniform cylinder is determined by measuring its mass m , length l and… JEE Main 2026 Four persons measure the length of a rod as 20.00 ~cm, 19.75 ~cm, 17.01 ~cm and 18.25 cm.… JEE Main 2026 In an experiment the values of two spring constants were measured as k_ 1 =(10 ± 0.2) N /… JEE Main 2026 Length, breadth and thickness of a strip having a uniform cross section are measured to… JEE Advanced 2025 A quantity Q is formulated as X^ -2 Y^ +(3)/(2) Z^ -(2)/(5) · X, Y and Z are independent… JEE Main 2025 A physical quantity C is related to four other quantities p, q, r and s as follows C=… JEE Main 2025 A physical quantity Q is related to four observables a, b, c, d as follows : Q= ab ^4 ~cd… JEE Main 2025 For an experimental expression y=(32.3 × 1125)/(27.4) , where all the digits are… JEE Main 2025 Full Mathematics in Physics list All JEE Main PYQs