Question

A solid cube has volume $(1000\pm 0.3)$ $c{m}^3$. The side of the cube is

• A. $(10\pm 0.1)$ $cm$
• B. $(10\pm 0.01)$ $cm$
• C. $(10\pm 0.001)$ $cm$
• D. $(10\pm 0.003)$ $cm$

Answer 1

The correct option is C $(10\pm 0.001)$ $cm$

$V=X^3$

$\Rightarrow \ln V=3\ln X$

$V=(1000\pm 0.3)$ $c{m}^3$

$\frac{dV}{V}=3\frac{dX}{X}$

$\Rightarrow dX=\frac{dV}{V}\times \frac{X}{3}=\frac{0.3}{1000}\times \frac{10}{3}=0.001$

$X=(10\pm 0.001)$ $cm$