# The Circumference of a Circle is 8 Cm. Find the Area of the Sector Whose Central Angle is 72°. - Mathematics

Sum

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

#### Solution

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 cm.

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 cm

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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 18 Area of Circle, Sector and Segment
Exercise 18A | Q 18 | Page 820