SOLUTION: PLS. HELP ME SOLVE THIS PROBLEM. TNX PROB. 1 IN A CIRCLE OF RADIUS 6 INCHES, THE LENGTH OF THE ARC OF A SECTOR IS 6PIE INCHES. WHAT IS THE AREA OF THE SECTOR? PROB. 2. FIND TH

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Question 380947: PLS. HELP ME SOLVE THIS PROBLEM. TNX
PROB. 1 IN A CIRCLE OF RADIUS 6 INCHES, THE LENGTH OF THE ARC OF A SECTOR IS 6PIE INCHES. WHAT IS THE AREA OF THE SECTOR?
PROB. 2. FIND THE CENTRAL ANGLE OF A CIRCLE WHICH INTERCEPTS AN ARC 80PIE CENTIMETER WITH THE RADIUS OF THE CIRCLE IS 20 CENTIMETER.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
I believe I answered the first part of your question.
If not, let me know and I will do it again.
You should already have the answer for that part.

The second part of your question is:

FIND THE CENTRAL ANGLE OF A CIRCLE WHICH INTERCEPTS AN ARC 80PIE CENTIMETER WITH THE RADIUS OF THE CIRCLE IS 20 CENTIMETER.
The general formula for determining the length of an arc is:

L = x/360 * C

L equals the length of the arc.
x = the number of degrees of the arc
C = the circumference of the circle from where the arc was drawn.

C = 2 * pi * r

r = the radius of the circle.

C is also equal to the length of an arc of 360 degrees.

In your problem, you are given that the radius of the circle from which the arc as drawn is equal to 20 centimeters.

This makes the circumference of that circle equal to 2 * pi * 20 = 40 * pi.

Your formula for the length of the arc becomes:

L = x/360 * 40 * pi

You know the length of your arc.

That is given as 80 * pi.

Your formula becomes:

80 * pi = x/360 * (40 * pi)

Divide both sides of this equation by (40 * pi) and you get:

(80 * pi) / (40 * pi) = x/360

This becomes:

2 = x / 360

Multiply both sides of this equation by 360 and you get:

x = 720 degrees.

That's your answer.