Part 1) A 20° sector in a circle has an area of 21.5π yd².
What is the area of the circle?
we know that
the area of a circle represent a sector of [tex]360[/tex] degrees
so by proportion
[tex]\frac{21.5\pi }{20} =\frac{x}{360} \\ \\ x*20=360*21.5\pi \\ \\x=(360*21.5*3.14)/20\\ \\x= 1,215.18\ yd^{2}[/tex]
therefore
the answer part 1) is
The area of the circle is [tex]1,215.18\ yd^{2}[/tex]
Part 2) What is the area of a sector with a central angle of 3π/5 radians and a diameter of 21.2 cm?
we know that
the area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
where
r is the radius of the circle
in this problem we have
[tex]Diameter=21.2\ cm\\ r=Diameter/2\\r=21.2/2\\r= 10.6\ cm[/tex]
Find the area of the circle
[tex]A=\pi r^{2}[/tex]
[tex]A=\pi*10.6^{2}[/tex]
[tex]A=352.8104\ cm^{2}[/tex]
Find the area of the sector
we know that the area of the circle represent a sector of [tex]2\pi[/tex] radians
by proportion
[tex]\frac{352.8104}{2\pi }=\frac{x}{(3\pi/5)} \\\\x*2\pi=(3\pi*352.8104)/5\\ \\x= 105.84\ cm^{2}[/tex]
therefore
the answer part 2) is
the area of the sector is
[tex]105.84\ cm^{2}[/tex]
