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Question
The length of an arc of a circle, subtending an angle of 54° at the centre, is 16.5 cm. Calculate the radius, circumference and area of the circle.
Solution
Length of the arc = 16.5 cm
θ = 54°
Radius = ?
Circumference=?
We know:
Length of the arc `=( 2pi"r"theta)/360`
`= 16.5 = (2xx22/7xx"r"xx54)/360`
`=> "r" = (16.5xx360xx7)/(44xx54)`
⇒ r = 17.5 cm
c = 2πr
`= 2xx22/7xx17.5 `
= 110 cm
Circumference = 110 cm
Now,
Area of the circle = πr2
`=22/7xx17.5xx17.5`
= 962.5 cm2
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