Question

The length of the arc of a circle subtenteding an angle 54degree at the center is 16.5cm calculate the radius,circumference and area of the circle

Answer 1

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The length of the arc of a circle subtenteding an angle 54degree at the center is 16.5cm calculate the radius,circumference and area of the circle

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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

Step-by-step explanation:

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