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 r be radius and l be the slant height of a cone, then curved surface area =$\pi rl$

If slant height is increased by 10%, then new slant height, $l^{\prime }=l+\frac{10}{100}l=\frac{11l}{10}$

New curved surface area =$\pi r\frac{11l}{10}=\frac{11}{10}\left(\pi rl\right)$

Increase in surface area =$\frac{11}{10}\left(\pi rl\right)-\left(\pi rl\right)=\frac{1}{10}\pi rl$

$\%increase=\frac{1}{10}\pi rl\times \frac{100}{\pi rl}=10\%$