Question

A right angled triangle having its base and height equal to 24 $cm$ and 7 $cm$ respectively is rotated by 360⁰ along its base. Find the curved surface area of the resultant figure.

• A. $520c{m}^2$
• B. $550c{m}^2$
• C. $450c{m}^2$
• D. $1460c{m}^2$

Answer 1

The correct option is B $550c{m}^2$

When a right angled triangle is rotated by ${360}^0$ along its base, it forms a cone.

By Pythagoras theorem, the slant height:
$l^2=h^2+r^2$
$\Rightarrow l=\sqrt{{24}^2+7^2}$
$\Rightarrow l=25cm$

When triangle rotates around its base, radius will be 7 $cm$.

So, curved surface area
$=\pi rl$
$=\frac{22}{7}\times 7cm\times 25cm$
$=550c{m}^2$