Question

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

What is the area of the circle?
Use 3.14 for pi.
2.)What is the area of a sector with a central angle of 3π/5 radians and a diameter of 21.2 cm?
Use 3.14 for π and round your final answer to the nearest hundredth.

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

`(21.5\pi )/(20) =(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

`(352.8104)/(2\pi )=(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)`