Area of a sector of a circle of radius 36 cm is 54 π cm². Find the length of the corresponding arc of the sector
Solution:
Given, the area of the sector of a circle is 54π square cm.
The radius of circle, r = 36 cm
We have to find the length of the corresponding arc of the sector.
Area of sector = πr²θ/360°
54π = π(36)²θ/360°
Cancelling common term on both sides,
54 = (36)²θ/360°
Solving for θ,
θ = 54(360°)/(36)²
= 54(10)/36
= 540/36
θ = 15°
Length of the arc = θ/360°(2πr)
= (15°/360°)(2π)(36)
= (1/24)(2π)(36)
= 36π/12
= 3π
Therefore, the length of the arc is 3π cm.
✦ Try This: Area of a sector of a circle of radius 10 cm is 40 π cm² . Find the length of the corresponding arc of the sector.
Given, the area of the sector of a circle is 40π square cm.
The radius of circle, r = 10 cm
We have to find the length of the corresponding arc of the sector.
Area of sector = πr²θ/360°
40π = π(10)²θ/360°
Cancelling common term on both sides,
40 = (100)θ/360°
Solving for θ,
θ = 40(360°)/(100)
= 4(36)
θ = 144°
Length of the arc = θ/360°(2πr)
= (144°/360°)(2π)(10)
= 4(2π)
= 8π
Therefore, the length of the arc is 8π cm.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12
NCERT Exemplar Class 10 Maths Exercise 11.3 Sample Problem 4
Area of a sector of a circle of radius 36 cm is 54 π cm². Find the length of the corresponding arc of the sector
Summary:
Area of a sector of a circle of radius 36 cm is 54 π cm². The length of the corresponding arc of the sector is 3π cm
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