Question

The slant height of a cone is increased by $10\%$. If the radius remains the same, the curved surface area is increased by _____.

• A. $10\%$
• B. $12.1\%$
• C. $20\%$
• D. $21\%$

Answer 1

The correct option is A $10\%$

Let 'l' be the slant height of the cone.
Initial curved surface area $=\pi rl$
New slant height $=l+\frac{10}{100}\times l$
$=1.1l$
New curved surface area $=\pi r\times \left(1.1\right)l$
$\therefore$ Percentage increase in curved surface area
$=\frac{Newcurvedsurfacearea-initialcurvedsurfacearea}{Initialsurfacearea}\times 100$
$=\frac{1.1\pi rl-\pi rl}{\pi rl}\times 100$
$=10\%$