SOLUTION: find the area of the largest square that can be cut from a sector of a circle radius 8 cm and a central 120 degree

Question 1116483: find the area of the largest square that can be cut from a sector of a circle radius 8 cm and a central 120 degree
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!




Let the square be ABCD.

Side of the square = AB = PQ = 2OQ.

Since triangle OBQ is a 30�,60�,90� triangle, its longer
leg is  times its shorter leg.

We let its shorter leg BQ be x, then its longer leg OQ
is .

Since  = OQ = PQ/2 = AB/2,

BC = 2∙OQ = .

OC = radius = 8

Using Pythagorean theorem on right triangle OQC

OQ� + QC� = OC�



Solve that and get 



So one side of the square is twice that, or 2x, which is

 = side of square.

Therefore the area of the square is



or 



Edwin

RELATED QUESTIONS
Find the area in square centimeter of the largest square that can be cut from a sector of (answered by greenestamps)

the area of a sector of a circle with radius 7 cm is 15 square cm .find the measure of... (answered by ankor@dixie-net.com)

The area of a sector of a circle with the radius 7cm is 15 square cm. Find the measure of (answered by Theo)

in a circle with radius 6 cm, find the exact area of a sector whose central angle measure (answered by MathLover1)

A sector of a circle has a central angle of 50 degrees and an area of 650 cm^2. Find the... (answered by mananth)

If the sector formed by a central angle of 45� has an area of π/2 square... (answered by josgarithmetic)

find the area of a sector of a circle, given the radius is 46mm and whose central angle... (answered by Cromlix)

Find the length of an arc and area of a sector of a circle of radius 30 cm, central angle (answered by Alan3354)

Find the area of a sector defined by a central angle of 36 degrees and a radius of 10... (answered by jim_thompson5910)