Given the dartboard of diameter , divided into 20 congruent sectors,
- The central angle is
- The fraction of a circle taken up by one sector is
- The area of one sector is to the nearest tenth
The area of a circle is given by the formula
A sector of a circle is a fraction of a circle. The fraction is given by . Where is the angle subtended by the sector at the center of the circle.
The formula for computing the area of a sector, given the angle at the center is
<h3>Given information</h3>
We given a circle (the dartboard) with diameter of , divided into 20 equal(or, congruent) sectors
<h3>Part I: Finding the central angle</h3>
To find the central angle, divide by the number of sectors. Let denote the central angle, then
<h3>Part II: Find the fraction of the circle that one sector takes</h3>
The fraction of the circle that one sector takes up is found by dividing the angle a sector takes up by . The angle has already been computed in Part I (the central angle, ). The fraction is
<h3>Part III: Find the area of one sector to the nearest tenth</h3>
The area of one sector can be gotten by multiplying the fraction gotten from Part II, with the area formula. That is
Learn more about sectors of a circle brainly.com/question/3432053