Question

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

Answer 1

Answer:

$105.84\ cm^2$

Step-by-step 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

$\frac{112.36\pi}{360^o}=\frac{x}{108^o}\\\\x=112.36\pi(108)/360\\\\x=33.708\pi\ cm^2$

assume

$\pi=3.14$

substitute

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