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.

Answer 1

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