Q1 of 18 Page 173

In a circle, the length of an arc of central angle 40° is 3π centimetres. What is the perimeter of the circle? What is its radius?

X = 40°


Length of arc = 3cm


In a circle of radius r,


If central angle = x°


Length of arc =


Putting in above equation,


3 =


∴ 3 =


∴ = r


∴ r≈3 cm


If r = radius of circle,


Perimeter = 2 × π × r


Hence, Perimeter = 2 × π × 3 ≈18.84 cm


More from this chapter

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1

In the pictures, below, find the difference between the areas of the circle and the polygon, up to two decimal places:

 2

The pictures below show circles through the vertices of a square and a rectangle:


Calculate the areas of the circles.

 2

In the same circle, what is the length of an arc of central angle 25° is 4 centimetres.

i) In the same circle, what is the length of an arc of central angle 75°?


ii) In a circle of radius one and a half times the radius of this circle, what is the length of an arc of central angle 75°?

 3

From a bangle of radius 3 centimetres, a piece is to be cut out to make a ring of radius centimetres.

i) What should be the central angle of the piece to be cut out?


ii) The remaining part of the bangle was bent to make a smaller bangle. What is its radius?