Question

The area of a sector with radius 4 cm and central angle $60$ degrees is

• A. $\frac{2\pi }{3}c{m}^2$
• B. $\frac{4\pi }{3}c{m}^2$
• C. $\frac{8\pi }{3}c{m}^2$
• D. $\frac{16\pi }{3}c{m}^2$

Answer 1

The correct option is C $\frac{8\pi }{3}c{m}^2$

The central angle $={60}^{\circ }.$

Since to make a complete circle it needs ${360}^{\circ }.$

So its $\frac{1}{6}th$ of the Area of the Sector

So the Area of the Sector $=\frac{1}{6}\ast pi{r}^2=\frac{1}{6}\ast \pi \ast 16=\frac{8\pi }{3}c{m}^2$