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

Given that

if Angle subtended at center is 54° , then length of the ARC = 16.5 cm

so if  Angle subtended at center is 1° , then length of the ARC = (16.5/54)cm

so if Angle substended at center is 360° ( full circle) ,

                                         then length of ARC that is circumfrence = (16.5/54) × 360°

                                          = 110 cm

So Circumference  of circle = 110 cm

circumference = 2πr

⇒ 110 = 2πr

⇒ 110 = 2 × (22/7) × r

⇒ r = (110 × 7)/(2 × 22) = 17.5 cm

so Radius = 17.5 cm

Area of circle = πr² = 22/7 × 17.5 × 17.5 = 962.5 cm²

Hence radius = 17.5 cm , circumference = 110 cm and area = 962.5 cm²

Answer 2

Answer:- Radius of circle is 17.5 cm.

Circumference of the circle is 110 cm.

Area of the circle is 962.5 square cm.