SOLUTION: A plastic cover is made for a pool with a diameter of 24 feet. The cover will rest on the top of the pool and will include a wedge-shaped flap that forms a 45 degree angle at the c

Algebra ->  Circles -> SOLUTION: A plastic cover is made for a pool with a diameter of 24 feet. The cover will rest on the top of the pool and will include a wedge-shaped flap that forms a 45 degree angle at the c      Log On


   

Question 78059: A plastic cover is made for a pool with a diameter of 24 feet. The cover will rest on the top of the pool and will include a wedge-shaped flap that forms a 45 degree angle at the center of the cover. A zipper will go along 1 side of the wedge-shape flap and around the arc. Which of the following is closest to the length, in feet, of the zipper?
-I know that 12 feet is the length of one radius so that is part of the length of the zipper. I am not sure how to find the length of the arc on a circle.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find the arc length simply use this formula:
where is the angle
So lets find the arc length with the given information:
Solved by pluggable solver: Arc Length
Angle at center described by an Arc


The angle described by an arc at center is 45 degrees.



Arc of a circle


The Length of Arc is given by formula


Length+=+pi%2Aradius%2Acentral+angle%2F180


Length+=+pi%2A12%2A45%2F180=9.42477795


Conversion of angles from degrees to radian:


The relation between two units of angle measurement is :


2*pi rad = 360 degrees


Area of Arc when angle in radians is,


Length=Central+angle%2Aradius


Length=0.7853981625%2A12=9.42477795


Hence, For a Circle of radius 12 the Arc length is 9.42477795 when it subtends an angle of 45 degrees at center.


For more on this topic, See the lessons on Circles and their properties

Some relevant wikipedia articles for the topic.



So our arc length is 9.424778 ft
Since the zipper goes from the center to the arc, simply add the arc length and the radius to find the total length of the zipper:
12+9.424778=21.424778 ft
So if you wanted this length rounded to the closest foot you would get:
lenght of zipper=21 ft