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.

Consider the Circle shown above,

We know, Length of arc of sector

Where R = radius of circle and θ = central angle of the sector

Given, Length of arc = ℓ = 16.5 cm and θ = 54^{o}. Let the radius be x cm

Put the values of ℓ and θ in equation 1

On rearranging

⇒ x = 17.5 cm

Also, we know circumference of the circle = 2πR

⇒ Circumference of the circle = 2πx (put value of x in this equation)

⇒ Circumference of the circle = 2π(17.5)

⇒ Circumference of the circle = 110 cm

Also, we know Area of the circle = πR^{2}

⇒ Area of the circle = πx^{2}

⇒ Are of the circle = π(17.5^{2})

⇒ Area of the circle = 962.5 cm^{2}

The radius of circle is 17.5 cm, circumference is 110 cm and area is 962.5 cm^{2}

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