Question

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

• A. 251 cc
• B. 25.1cc
• C. 2.51 cc
• D. 251.2cc

Answer 1

The correct option is B 25.1cc

Given that,

$r=10$

$\Delta r=0.02$

We know that,

The volume of sphere is

$V=\frac{4}{3}\pi r^3$

$V=\frac{4}{3}\times 3.14\times {\left(10\right)}^3$

$V=4186.7cc$

Now, taking log

$\log V=\log \frac{4}{3}+3\log r$

Differentiating on both sides

$\frac{\Delta V}{V}=0+3\frac{\Delta r}{r}$

Now, the error is

$\frac{\Delta V}{V}=3\times \frac{\Delta r}{r}$

$\Delta V=V\times 3\times \frac{\Delta r}{r}$

$\Delta V=4186.7\times 3\times \frac{0.02}{10}$

$\Delta V=25.1cc$

Hence, the error in the measurement of its volume is $25.1$ cc