JEE MAIN - Physics (2019 - 10th January Evening Slot - No. 23)
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 ?
4264.4 $$ \pm $$ 81.0 cm3
4264 $$ \pm $$ 81 cm3
4300 $$ \pm $$ 80 cm3
4260 $$ \pm $$ 80 cm3
Explanation
Volume of cylinder(V) = $$\pi $$r2h
= $$\pi {{{d^2}} \over 4}h$$
= $$3.14 \times {{{{\left( {12.6} \right)}^2}} \over 4} \times 34.2$$
= 4260
$${{\Delta V} \over V} = 2{{\Delta d} \over d} + {{\Delta h} \over h} = 2\left( {{{0.1} \over {12.6}}} \right) + {{0.1} \over {34.2}}$$ = 0.0188
$$ \therefore $$ $$\Delta $$V = 0.0188 $$ \times $$ 4260 = 80
= $$\pi {{{d^2}} \over 4}h$$
= $$3.14 \times {{{{\left( {12.6} \right)}^2}} \over 4} \times 34.2$$
= 4260
$${{\Delta V} \over V} = 2{{\Delta d} \over d} + {{\Delta h} \over h} = 2\left( {{{0.1} \over {12.6}}} \right) + {{0.1} \over {34.2}}$$ = 0.0188
$$ \therefore $$ $$\Delta $$V = 0.0188 $$ \times $$ 4260 = 80
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