Question

What is the area of a sector with a central angle of π3 radians and a radius of 12.4 m? Use 3.14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box.

Answer 1

The answer to this is 80.47. I just took the quiz.

Answer 2

Answer: $80.47\ m^2$

Step-by-step explanation:

The area of a sector is given by :-

$\text{Area of sector}=\frac{\theta}{2}\times( r^2), \text{where }\theta\text{ is measure of central angle in radians.}$

Given :Central angle = $\theta=\frac{\pi}{3}$

radius = 12.4 m

Then,

$\text{Area of sector}=\frac{\frac{\pi}{3}}{2}\times( (12.4)^2)\\\\\Rightarrow\ \text{Area of sector}=\frac{\pi}{6}\times153.76\\\\\Rightarrow\ \text{Area of sector}=\frac{3.14}{6}\times153.76\\\\\Rightarrow\ \text{Area of sector}=80.4677333333\approx80.47\ m^2$