Question
Download Solution PDFThe area of the sector of a circle of radius 28 cm is 112 cm2. Find the length of the corresponding arc of the sector.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The area of the sector of a circle of radius 28 cm is 112 cm2.
Calculation:
Area of sector = πr²θ/360°
112 = π(28)²θ/360°
θ = 360/22
Length of the arc = θ/360°(2πr)
⇒ 360/360 × 22/22 × 28/7 × 2
⇒ 8 cm
Therefore, the length of the arc is 8 cm.
Alternate Method Area of sector = 1/2 × r × l
r = radius of the circle
l = length of arc
As per question,
⇒ 112 = 1/2 × 28 × l
⇒ l = 8 cm
Therefore, the length of the arc is 8 cm.
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