Q2 of 18 Page 167

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


Calculate the areas of the circles.

For figure 1,



Side of square = 3 cm


If, Side of square = a cm


Diagonal of square = =


As seen in figure,


Diameter of circle = Diagonal of square


∴ Diameter of circle = √2 × 3 cm


∴ Radius of circle =


If r = radius of circle


Area of circle = π × r2 cm2


= ()2


= cm2


≈3.144.5


≈14.13 cm2


For figure 2,



From Pythagoras theorem,


(Hypotenuse)2 = (one side)2 + (other side)2


Diagonal of rectangle = (42 + 22)1/2


= (16 + 4)1/2


= √20 cm


As seen from figure,


Diagonal of rectangle = Diameter of circle = √20 cm


∴ Radius of circle =


If r = radius of circle


Area of circle = π × r2 cm2


= ()2


= cm2


≈3.1415200


≈628.3 cm2


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

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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?

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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°?