Question

What is the area of a sector with a central angle of 160 degrees and a diameter of 5.8 m?

Answer 1

Diameter=5.8
Radius= 2.9

Area= 2.9*2.9*pi=8.41pi

8.41pi*160/360~11.74

Answer 2

Answer: 11.7 sq. m.

Explanation:

The area of sector with angle x and radius r is given by :-

`\text{Area of sector}=(x)/(360^(\circ))\pi r^2`

Given: Diameter = 5.8 m

Then, radius =
`(5.8)/(2)=2.9\ m`

Now, the area of sector with angle 160° and radius 2.9 is given by :-

`\text{Area of sector}=(160^(\circ))/(360^(\circ))\pi (2.9)^2\\\\\Rightarrow\ \text{Area of sector}=\frac{160{\circ}}{360^(\circ)}(3.14)(2.9)^2\\\\\Rightarrow\ \text{Area of sector}=11.7366222222\approx 11.7\ m^2`