Question

1.) A 20° sector in a circle has an area of 21.5π yd².

Answer 1

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 $360$ degrees

so by proportion

$\frac{21.5\pi }{20} =\frac{x}{360} \\ \\ x*20=360*21.5\pi \\ \\x=(360*21.5*3.14)/20\\ \\x= 1,215.18\ yd^{2}$    

therefore

the answer part 1) is

The area of the circle is $1,215.18\ yd^{2}$

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

$A=\pi r^{2}$

where

r is the radius of the circle

in this problem we have

$Diameter=21.2\ cm\\ r=Diameter/2\\r=21.2/2\\r= 10.6\ cm$

Find the area of the circle

$A=\pi r^{2}$

$A=\pi*10.6^{2}$

$A=352.8104\ cm^{2}$

Find the area of the sector

we know that the area of the circle represent a sector of $2\pi$ radians

by proportion

$\frac{352.8104}{2\pi }=\frac{x}{(3\pi/5)} \\\\x*2\pi=(3\pi*352.8104)/5\\ \\x= 105.84\ cm^{2}$

therefore

the answer part 2) is

the area of the sector is

$105.84\ cm^{2}$