Math CentralQuandaries & Queries


Question from Wallis, a student:

I have more then a quarter of a circle, but less than half. What is the circumference if the two side are 7cm and the angle between them is 110 degrees?

Hi Wallis,

The circumference of a circle is 2 times pi times r where r is the radius. Thus your circle has a circumference of

2 times pi times 7 = 14 pi centimeters.

But, as you said, the sector you have is more than a quarter of this but less than half. Since all the way around the circle is 360 degrees the fraction of the circle you have is 110/360. Thus the length of your arc is

110/360 times 14 pi centimeters.


About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS