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. - Mathematics

Sum

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°

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 cm

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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 18 Area of Circle, Sector and Segment
Exercise 18A | Q 13 | Page 831