Question

On heating a uniform metallic cylinder length increases by 3%. The area of cross-section of its base will increase by

• A. 1.5%
• B. 3%
• C. 9%
• D. 6%

Answer 1

The correct option is C 9%

According to the question,

The area of the base is $\pi r^2$ or $\frac{\pi d^2}{4}$ where $r$ is the radius and $d$ is the diameter.

So, we have $r$ or $d$ both of have the dimension of length,

$A=\pi r^2$

$\delta A=3\pi r^2\times \delta r$

$=\frac{\delta A}{A}$

$=3\times \left(\frac{\delta r}{r}\right)$

So, it is given that $\frac{\delta r}{r}=3\%$

Hence,

$\frac{\delta A}{A}3\times 3\%$

$=9\%$

So, the area of the cross- section of its base will increase by $9\%$.