Question

Find the area of a sector with a central angle of 170° and a diameter of 9.1 cm. Round to the nearest tenth.

Answer 1

The area of sector is 30.7 cm².

Explanation:

The diameter of a circle is 9.1 cm, so the radius of the circle is

`r=(d)/(2)=(9.1)/(2)=4.55`

The central angle of a sector is 170°.

The area of a sector is

`A=\pi r^2* ((\theta)/(360))`

Where, r is radius and θ is central angle.

`A=\pi (4.55)^2* ((170)/(360))`

`A=30.712777`

`A\approx 30.7`

Therefore the area of sector is 30.7 cm².

Answer 2

A central angle:
α = 170°
d = 9.1 cm
r = 9.1 : 2 = 4.55 cm
Area of a sector:
A = r² π α / 360°
A = ( 4.55 )² · 3.14 · 170° / 360°
A = 30.7 cm²