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# Area of a sector of central angle 200° of a circle is 770 cm². Find the length of the corresponding arc of this sector

**Solution:**

Given, central angle θ = 200°

Area of sector of a circle = 770 cm²

We have to find the length of the corresponding arc of this sector.

Area of sector = πr²θ/360°

770 = (22/7)r²(200°/360°)

Solving for r,

r² = (770(7)/22)[360°/200°]

r² = (70(7)/2)[9/5]

r² = 35(7)(9/5)

r² = 7(7)(9)

r² = 49(9)

Taking square root,

r = 7(3)

r = 21 cm

So, the radius of the sector = 21 cm.

Length of the arc = θ/360°(2πr)

= (200°/360°)(2)(22/7)(21)

= (5/9)(44)(3)

= 5(44)/3

= 220/3

= 73.33 cm²

Therefore, the length of the corresponding arc is 73.33 cm²

**✦ Try This: **Area of a sector of central angle 120° of a circle is 500 cm . Find the length of the corresponding arc of this sector.

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 12

**NCERT Exemplar Class 10 Maths Exercise 11.4 Problem 15**

## Area of a sector of central angle 200° of a circle is 770 cm². Find the length of the corresponding arc of this sector

**Summary:**

Area of a sector of central angle 200° of a circle is 770 cm². The length of the corresponding arc of this sector is 73.33 cm²

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