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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