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What is the area of a sector with a central angle of 2pi/9 radians and a diameter of 20.6mm? Use 3.14 for Ali and round your answer to the nearest hundredth.

What is the area of a sector with a central angle of 2pi9 radians and a diameter of 206mm Use 314 for Ali and round your answer to the nearest hundredth class=

Respuesta :

carlosego
- The area of the circle is:

 A=πr²

 A is the area of the circle.
 π=3.14
 r is the radius of the circle.

 - To calculate the area of  the sector indicated in the problem, you must apply the following formula:

 As=(θ/2π)πr²

 As is the area of the sector.
 θ is the central angle (θ=2π/9)
 π=3.14
 r is the radius.

 - First, you must find the radius:

 r=Diameter/2
 r=20.6 mm/2
 r=10.3 mm

 - Now, you can substitute the values into the formula As=(θ/2π)πr². Then, you have:

 As=(θ/2π)πr²
 As=(2π/9/2π)(π)(10.3)²
 As=(π/9π)(π)(10.3)²
 As=(3.14/9x3.14)(3.14)(10.3)²

 - Finally, the area of the sector is:

 As= 37.01 mm²

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