Question 178: 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: