The relative error in the determination of the surface area of a sphere is α . Then the relative error in the determination of its volume is

Correct answer: C. (3)/(2) α Relative error in Surface area, Δ s s =2 × Δ r r =α and relative error in volume, Δ v v =3 × Δ r r Relative error in volume w.r.t. relative error in area, Δ v v =(3)/(2) α

JEE Main 201815 AprilMorning ShiftOnline

Exam: JEE Main
Year: 2018
Date: 15 April
Shift: Morning Shift
Mode: Online
Subject: Physics
Chapter: Mathematics in Physics

JEE Main 2018 · 15 April · Morning Shift · Online · Physics · Mathematics in Physics

The relative error in the determination of the surface area of a...

The relative error in the determination of the surface area of a sphere is

\alpha

. Then the relative error in the determination of its volume is

Options

A $\frac{2}{3} \alpha$
B $\frac{2}{3} \alpha$
C $\frac{3}{2} \alpha$
D $\alpha$

Correct answer

C. $\frac{3}{2} \alpha$

Step-by-step solution

Relative error in Surface area,

\frac{\Delta \mathrm{s}}{\mathrm{s}}=2 \times \frac{\Delta \mathrm{r}}{\mathrm{r}}=\alpha

and relative error in volume,

\frac{\Delta \mathrm{v}}{\mathrm{v}}=3 \times \frac{\Delta \mathrm{r}}{\mathrm{r}}\therefore

Relative error in volume w.r.t. relative error in area,

\frac{\Delta \mathrm{v}}{\mathrm{v}}=\frac{3}{2} \alpha

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