Question

The radius of a circle is 9 miles. What is the area of a sector bounded by a 180° arc?

Answer 1

A of half circle= 1/2*pi*r^2
=81/2*pi=127.17 square miles

Answer 2

`\huge\boxed{\sf Area = 127.2\ miles\²}`

Explanation:

Given:

Radius = r = 9 miles

Degrees = 180°

Required:

Area of Sector = ?

Formula:

`\sf Area \ of \ Sector = (1)/(2)r^2 \theta`

Solution:

Firstly convert degree into radians

Radian =
`\sf (\pi)/(180) * 180`

Radian = π

Radian = 3.14 radians

Now, Find Area of sector

Area =
`(1)/(2) (9)^2 (3.14)`

Area = (81*3.14)/2

Area = 254.5 / 2

Area = 127.2 miles²

`\rule[225]{225}{2}`

Hope this helped!

~AH1807