Question on Minor arc & minor segment. Circle

Question

OA and OB are radii of the circle with centre O. The length of the radius is 25cm, and the angle AOB is 165 0. Show all information on a sketch. Find the area of the minor sector AOB, the length of the minor arc AB and the area of the minor segment AB.

Answer 1

OK, for this one you have to remember what the terms mean. When you cut two radii into the circle, you cut the circle into two pieces: the major and minor sectors. The minor sector is the small one. Its area is proportional to that of the whole circle according to the angle of the sector, like this:

 

sector area = (165 degrees / 360 degrees) circle area

= 0.4583 circle area

 

And the circle area is π r², which for r = 25 cm would be 625 π cm².

 

So the area of the minor sector is

 

0.4583 (625 π) = 900 cm²

 

Cheers!