Question

If the percentage error in the edge of a cube is 1, then error in its volume is

• A. $1\%$
• B. $2\%$
• C. $3\%$
• D. none of these

Answer 1

Answer: (C)

$3\%$

Volume of cube $V=x^3$

$\Rightarrow \frac{dV}{dx}=3x^2$

Percentage error in x is 1%.

$\Rightarrow \frac{\Delta x}{x}=\frac{1}{100}$

$\Rightarrow \Delta x=\frac{x}{100}$

Approximate error in V $=dV=\left(\frac{dV}{dx}\right)\Delta x$

$=\frac{3x^3}{100}$

Percentage error in V $=\frac{dV}{V}$

$=\frac{3}{100}=3\%$