Question

Find the area of sector and length of arc of sector.

• A. 20
• B. 14
• C. Area of sector
  $=\frac{2\pi r}{360}\times \theta =\frac{\theta }{360}\times 2\pi r$
• D. Length of the arc $=\frac{\pi r^2}{360}\times \theta =\frac{\theta }{360}\times \pi r^2$

Answer 1

Answer: (A), (B)

The correct options are
A

20

B

14

Circle is also a sector subtending an angle of ${360}^{\circ }$ at the centre.

So, when the degree measure of the angle at the centre is 1, area of the sector
$=\frac{\pi r^2}{360}$

Therefore, when the degree measure of the angle at the centre is $\theta$,

Area of the sector
$=\frac{\pi r^2}{360}\times \theta =\frac{\theta }{360}\times \pi r^2$

Arc of a sector is a part of the circumference.

When the degree measure of the angle at the centre is 1, the length of the arc
$=\frac{2\pi r}{360}$

Therefore, when the degree measure of the angle at the centre is $\theta$,

Length of the arc
$=\frac{2\pi r}{360}\times \theta =\frac{\theta }{360}\times 2\pi r$