MATH SOLVE

4 months ago

Q:
# 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.

Accepted Solution

A:

- 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

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