Question

What is the area of a sector with a central angle of 4π5 radians and a radius of 11 cm?

Answer 1

Answer: 151.98 I just took the test!

Step-by-step explanation:

Answer 2

Answer

Area of sector (A) is given by:

$A = \pi r^2 \cdot \frac{\theta}{360^{\circ}}$

where,

r is the radius and $\theta$ is the angle in degree.

As per the statement:

A central angle of $\frac{4 \pi}{5}$ radians and a radius of 11 cm.

⇒r = 11 cm

Use conversion:

1  radian = $\frac{180}{\pi}$

then;

$\frac{4 \pi}{5}$ radians = $\frac{180}{\pi} \times \frac{4 \pi}{5} = 144^{\circ}$

⇒$\theta = 144$ degree

Substitute these given values and use 3.14 for π we have;

$A = 3.14 \cdot 11^2 \cdot \frac{144}{360} = 379.94 \cdot 0.4 = 151.976$ square cm.

Therefore, the area of a sector is, 151.976 square cm