Q. 134.9( 7 Votes )

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 :



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 = 54o. 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 = πR2


Area of the circle = πx2


Are of the circle = π(17.52)





Area of the circle = 962.5 cm2


The radius of circle is 17.5 cm, circumference is 110 cm and area is 962.5 cm2


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