Question

Volume of a cylinder increases by $6\%$ upon heating. The area of its curved surface will increase by

• A. $1\%$
• B. $6\%$
• C. $3\%$
• D. $4\%$

Answer 1

The correct option is D $4\%$

We know that, for a solid heated to raise the temperature by $\Delta T$
$\alpha :\beta :\gamma =1:2:3$
$\Rightarrow \frac{\Delta L}{L}$ : $\frac{\Delta A}{A}$ : $\frac{\Delta V}{V}=1:2:3......\left(1\right)$
Given, fractional change in volume of cylinder is $\frac{\Delta V}{V}=0.06$
From $\left(1\right)$, the fractional change in surface area of the cylinder is given by
$\frac{\Delta A}{A}=\frac{2}{3}\times \frac{\Delta V}{V}=0.04$
$\therefore$ The percentage increase in the value of curved surface area is $\frac{\Delta A}{A}\times 100=4\%$
Thus, option (d) is the correct answer.