Question

What is the area of a sector with a central angle of 108 degrees and a diameter of 21.2 cm?

Use 3.14 for it and round your final answer to the nearest hundredth.

Answer 1

`105.84\ cm^2`

Explanation:

step 1

Find the area of the circle

The area of the circle is

`A=\pi r^(2)`

we have

`r=21.2/2=10.6\ cm` ----> the radius is half the diameter

substitute

`A=\pi (10.6)^(2)`

`A=112.36\pi\ cm^2`

step 2

Find the area of a sector

Remember that

The area of the circle subtends a central angle of 360 degrees

so

using proportion

Find out the area of a sector with a central angle of 108 degrees

`(112.36\pi)/(360^o)=(x)/(108^o)\\\\x=112.36\pi(108)/360\\\\x=33.708\pi\ cm^2`

assume

`\pi=3.14`

substitute

`33.708(3.14)=105.84\ cm^2`