Question

The circumference of a circle is 8 cm. Find the area of the sector whose central angle is 72°.

Answer 1

Let the radius of the circle be r.
​Now,

Circumference = 8

⇒ 2πr = 8 

`⇒ r = 14/11 "cm"`

We have `r = 14/11 "cm" and theta = 72°`

Area of sector` = theta/360^circ xxpi"r"^2 = 72^circ/360^circxx22/7xx(14/11)^2 = 1.02  "cm"^2`

Hence. the area of the sector of the circle is 1.02 cm² .

Disclaimer : If we take the circumference of the circle is 8 cm then the area of the sector will be 1.02 cm². But if we take the circumference of the circle is 88 cm then the area of the sector will be 123.2 cm²