Question

In a circle of radius 10.5 cm, the minor arc is one-fifth of the major arc. Find the area of the sector corresponding to the major arc.

Answer 1

Let the length of the major arc be x cm

Radius of the circle = 10.5 cm

∴ Length of the minor arc`=x/5 "cm"`

Circumference `= (x + x/5) = "6x"/5  "cm"` 

Using the given data, we get : 

`(6x)/5 = 2xx22/7xx21/2`

`=>(6x)/5 = 66`

Or.

x = 55

∴ Area of the sector corresponding to the major arc `= (1/2xx55xx21/2) = 288.75  "cm"^2`