Question

If there is an error of $0.05cm$ in the measurement of the side as $2cm$ of a cube, then relative error in the volume is

• A. $0.075$
• B. $0.0075$
• C. $7.5$
• D. $0.75$

Answer 1

The correct option is A $0.075$

Volume of cube = $x^3$

$\frac{\Delta v}{\Delta x}=3x^2$

$[\Delta x=0.05cm$

$x=2cm]$

or $\frac{\Delta v}{v}=\frac{3x^2}{x^3}\Delta x=\frac{3}{x}\Delta x$

$=3\times \frac{0.05}{2}=3\times 0.025$

$=0.075$

$\therefore$ Relative error in volume = $0.075cm$