Question

The perimeter of a sector of a circle is $56$ cms and the area of the circle is $64\pi$ sq. cms Find the area of sector.

• A. $360c{m}^2$
• B. $160c{m}^2$
• C. $260c{m}^2$
• D. None of these

Answer 1

The correct option is B $160c{m}^2$

Area $=\pi r^2=64\pi c{m}^2$

$\Rightarrow r=8cm$

perimeter $=2r+r\theta$

perimeter of sector $=r(\theta +2)=56cm$

$\Rightarrow \theta =5rad$

Area of sector $=\frac{r^2\theta }{2}=\frac{64}{2}\times 5c{m}^2$

$=160c{m}^2$