Question

A right angled triangle having its base and height equal to 24 cm and 7 cm respectively is rotated by ${360}^{\circ }$ along its base. Find the curved surface area of 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 triangled is rotated by ${360}^{\circ }$ along its base, it forms a cone.
By Pythagoras theorem, slant height = $\sqrt{{24}^2+7^2}$ = 25 cm
When triangle rotates around its base, radius will be 7 cm.
So, curved surface area = $\pi rl=\frac{22}{7}\times 7cm\times 25cm=550c{m}^2$