Q4 of 18 Page 163

In this picture, the circles have the same centre and the line drawn is a diameter of the large circle. How much more is the perimeter of the large circle than the perimeter of the small circle?

The figure is shown below:



Diameter of larger circle = 1 cm


Hence, diameter of smaller circle = cm


Let r = Radius of smaller circle =


If r = radius of circle


Circumference =


As seen from figure,


Radius of Larger circle = 2r


Perimeter of smaller circle = 2 × π × r …(eq)2


Perimeter of larger circle = 2 × π × (2r) = 4 × π × r …(eq)1


Perimeter of larger circle is = (eq)1 – (eq)2


More then smaller circle by


= (4 × π × r) – (2 × π × r)


= 2 × π × r



More from this chapter

All 18 →
2

An isosceles triangle with its vertices on a circle is shown in this picture.


What is the perimeter of the circle?

 3

In all the pictures, below, centres of the circles are on the same line. In the first two pictures, the small circles are of the same diameter.


Prove that in all pictures, the perimeters of the large circle is the sum of the perimeters of the small circles.

 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.