**Circles calculate area circumference radius and diameter :**

Here we are going to see some example problems to understand how to calculate area and circumference of circle.

**Radius :**

The radius is a line segment with one end point at the centre and the other end on the circle. It is denoted by ‘r’.

**Diameter :**

Diameter is a chord passing through the centre of the circle. It is denoted by ‘d’.

The diameter is the longest chord. It is twice the radius.(i.e. d = 2r )

**Circumference of a circle:**

Can we find the distance covered by an athlete if he takes two rounds on a circular track. Since it is a circular track, we cannot use the ruler to find out the distance.

The distance around a circle is called the circumference of the circle, which is denoted by ‘C’. i.e., The perimeter of a circle is known as its circumference.

Circumference of circle = 2 π r

**Area of circle :**

The area of a circle is the number of square units inside that circle

Area of circle = π r²

**Example 1 :**

Find out the circumference of a circle whose diameter is 21 cm.

**Solution :**

**Diameter = 21 cm**

**Radius = 21/2 = 10.5 cm**

**Circumference of circle = **2 π r

= 2 (22/7) x 10.5

= 44 x 1.5

= 66 cm

Hence the circumference of circle is 66 cm.

**Example 2 :**

A wire of length 88 cm is bent as a circle. What is the radius of the circle.

**Solution :**

**Length of the wire = circumference of the circle**

2 π r = 88 cm

2 x (22/7) x r = 88

r = (88 x 7)/(2 x 22)

r = 14 cm

Hence the radius of the circle is 14 cm

**Example 3 :**

The diameter of a bicycle wheel is 63 cm. How much distance will it cover in 20 revolutions?

**Solution :**

When a wheel makes one complete revolutions,

Distance covered in one rotation = Circumference of wheel

Circumference of the wheel = 2πr units

= 2 x (22/7) x (63/2) cm

= 22 x 9 = 198 cm

For one revolution, the distance covered = 198 cm

For 20 revolutions, the distance covered = 20 × 198 cm

= 3960 cm

= 39 m 60 cm [100 cm = 1 m]

Hence the distance covered in 20 revolution is 39 m 60 cm

**Example 4 :**

A scooter wheel makes 50 revolutions to cover a distance of 8800 cm. Find the radius of the wheel.

**Solution :**

Distance travelled

= Number of revolutions/Circumference

2πr = 8800/50

2πr = 176

2 x (22/7) x r = 176

r = 176 x (7/22) x (1/2)

r = 28 cm

Hence the radius of the wheel is 28 cm

**Example 5 :**

The radius of a cart wheel is 70 cm. How many revolution does it make in travelling a distance of 132 m.

**Solution :**

Given: r = 70 cm, Distance travelled = 132 m.

Circumference of a cart wheel = 2πr

= 2 x (22/7) x 70

= 440 cm

Distance travelled

= Number of revolutions x Circumference

Number of revolutions

= Distance travelled/Circumference

= 132 m/440 cm

= 13200/440

= 30

Hence the number of revolution is 30.

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