 ## Book: RS Aggarwal - Mathematics

### Chapter: 18. Area of Circle, Sector and Segment

#### Subject: Maths - Class 10th

##### Q. No. 11 of Formative Assessment (Unit Test)

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11
##### A wire when bent in the form of an equilateral triangle encloses an area of 121√3 cm2. If the same wire is bent into the form of a circle, what will be the area of the circle? [Take π = 22/7]

Let the sides of equilateral triangle be a cm

Area of equilateral triangle = 121√3 cm2

Area of equilateral triangle = √3/4 × a2

√3/4 a2 = 121√3

a2 = 121√3 × 4/√3 = 121 × 4 cm2

a2 = 484 cm2

a = 22 cm

Perimeter of equilateral triangle = 3a

= 3 × 22 cm = 66 cm

Perimeter of equilateral triangle = Circumference of circle

Circumference of circle = 66 cm

Let the radius of circle be r

Circumference of circle = 2πr

2πr = 66 cm

2 × 22/7 × r = 66 cm

r = 66 × 1/2 × 7/22 cm

r = 10.5 cm

Area of circle = πr2 = 22/7 × 22/7 × 10.5 × 10.5 cm2

= 346.5 cm2

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