Question

In a circle, a sector is created by an arc measuring 54 degrees. If the diameter of the circle is 20 in, what is

a) the length of the arc

b) the area of the sector

Answer 1

a) 9.42 in

b) 47.1 sq. inches

Explanation:

`\sf \bf \theta = 54^\circ\\\\diameter = 20 \ in\\\\r = 20 / 2\\\\r = 10 \ in`

a) Length of arc:

`\boxed{\bf Lenght \ of \ arc = (\theta)/(360)*2\pi r}`

`= (54)/(360)*2*3.14*10\\\\= 9.42 \ in`

b) Area of sector:

`\boxed{\bf Area \ of \ sector = (\theta)/(360)*\pi r^2}`

`\bf = (54)/(360)*3.14*10*10\\\\= 47.1 \ in^2`