What is the area of a sector with a central angle of 4π5 radians and a radius of 11 cm?
2 answers:
Answer: 151.98 I just took the test!
Step-by-step explanation:
Answer
Area of sector (A) is given by:
![A = \pi r^2 \cdot \frac{\theta}{360^{\circ}}](https://tex.z-dn.net/?f=A%20%3D%20%5Cpi%20r%5E2%20%5Ccdot%20%5Cfrac%7B%5Ctheta%7D%7B360%5E%7B%5Ccirc%7D%7D)
where,
r is the radius and
is the angle in degree.
As per the statement:
A central angle of
radians and a radius of 11 cm.
⇒r = 11 cm
Use conversion:
1 radian = ![\frac{180}{\pi}](https://tex.z-dn.net/?f=%5Cfrac%7B180%7D%7B%5Cpi%7D)
then;
radians = ![\frac{180}{\pi} \times \frac{4 \pi}{5} = 144^{\circ}](https://tex.z-dn.net/?f=%5Cfrac%7B180%7D%7B%5Cpi%7D%20%5Ctimes%20%5Cfrac%7B4%20%5Cpi%7D%7B5%7D%20%3D%20144%5E%7B%5Ccirc%7D)
⇒
degree
Substitute these given values and use 3.14 for π we have;
square cm.
Therefore, the area of a sector is, 151.976 square cm
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