Question 206: Units , Dimensions and Error Analysis

Question

The diameter and height of a cylinder are measured by a meter scale to be 12.6 $ \pm $ 0.1 cm and 34.2 $ \pm $ 0.1 cm, respectively. What will be the value of its volume in appropriate significant figures ?

Accepted Answer

Volume of cylinder(V) = $\pi $r
2
h
= $\pi {{{d^2}} \over 4}h$
= $3.14 	imes {{{{\left( {12.6} ight)}^2}} \over 4} 	imes 34.2$
= 4260
${{\Delta V} \over V} = 2{{\Delta d} \over d} + {{\Delta h} \over h} = 2\left( {{{0.1} \over {12.6}}} ight) + {{0.1} \over {34.2}}$ = 0.0188
$ 	herefore $ $\Delta $V = 0.0188 $ 	imes $ 4260 = 80

Answer

4264.4 $ \pm $ 81.0 cm
3

Answer

4264 $ \pm $ 81 cm
3

Answer

4300 $ \pm $ 80 cm
3

Answer

4260 $ \pm $ 80 cm
3

Units , Dimensions and Error Analysis

The diameter and height of a cylinder are measured by a meter scale to be 12.6 \pm 0.1 cm and 34.2 \pm 0.1 cm, respectively. What will be the value of its volume in appropriate significant figures ?

Choose the correct answer: