SOLUTION: What is the central angle of a sector that is 40% of the pie chart

Algebra ->  Angles -> SOLUTION: What is the central angle of a sector that is 40% of the pie chart       Log On


   

Question 328758: What is the central angle of a sector that is 40% of the pie chart


Found 2 solutions by Fombitz, Theo:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
100% would be 360 degrees.
40%2F100=X%2F360
X=144 degrees

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
If it's 40% of the pie chart, then it takes up 40% of the area of the circle.

It also takes up 40% of the total degrees of the circle.

The total degrees of the circle is 360.

40% of 360 = .4 * 360 = 144 degrees.

The central angle will be 144 degrees.

The area of a circle is equal to pi * r^2

The area of a section of a circle is equal to x/360 * pi * r^2

Since x = 144, then the area of the section of the circle is equal to 144/ 360 * pi * r^2 which is equal to .4 * pi * r^2 which is equal to 40% of the area of the circle.

The simple answer is that 40% of the circle is 40% of the number of degrees in the circumference of the circle which is 40% of 360 which is 144.

If you divide the circle in half, then each half has 180 degrees.

If you divide the circle in fourths, then each fourth has 90 degrees.