Question

A chord of length $5\text{cm}$ subtends an angle of ${60}^{\circ }$ at the centre of a circle. The area of the sector of the same circle which is subtending central angle of ${120}^{\circ }$ at the centre, is

• A. $\frac{5\pi }{3}{\text{cm}}^2$
• B. $\frac{25\pi }{3}{\text{cm}}^2$
• C. $\frac{15\pi }{4}{\text{cm}}^2$
• D. $\frac{20\pi }{3}{\text{cm}}^2$

Answer 1

The correct option is B $\frac{25\pi }{3}{\text{cm}}^2$

If a chord makes an angle of ${60}^{\circ }$ at the centre of circle then the chord along with lengths of two radius makes an equilateral triangle.
$\therefore$ Radius of circle $=$ Length of chord $=5\text{cm}$

Area of sector making an angle of ${120}^{\circ }$ at the centre of circle of radius $5\text{cm}$
$=\frac{{120}^{\circ }}{{360}^{\circ }}\times \pi (5{)}^2$
$=25\pi \times \frac{1}{3}$
$=\frac{25\pi }{3}{\text{cm}}^2$

Hence, the correct answer is option b.