Question

The radius of the sphere is measured as $\left(10\pm 0.02\right)cm$. The error in the measurement of its volume is

• A. $25.1cc$
• B. $25.21cc$
• C. $2.51cc$
• D. $251.2cc$

Answer 1

The correct option is D $251.2cc$

Let $r$ be the radius of the sphere.

$\Rightarrow$ $r=10$

Error in the measurement of radius $=\Delta r$

$\therefore$ $\Delta r=0.02m$

$\Rightarrow$ Volume of the sphere $\left(V\right)=\frac{4}{3}\pi r^3$

We need to find error in calculating the volume that is $\Delta V$

$\Delta V=\frac{dv}{dr}\times \Delta r$

$=\frac{d\left(\frac{4}{3}\pi r^3\right)}{dr}\times \Delta r$

$=\frac{4}{3}\pi \frac{d\left(r^3\right)}{dr}\times \Delta r$

$=\frac{4}{3}\pi \left(3r^2\right)\times \left(\mathrm{0.0.2}\right)$

$=4\pi r^2\times 0.02$

$=4\times 3.14\times (10{)}^3\times 0.02$

$=251.2c{m}^3$ i.e. $251.2cc$