Class 7 Maths Perimeter and Area | Circles |

__Circles__

A circle is a simple closed shape where all points have the same distance from the centre. We have seen many shapes such as wheel, dining plate, coin etc. All these shapes are in the form of circle.

The center of a circle is the center point in a circle, from which all the distances to the points on the circle are equal. The radius is the distance from the center to any point on the circle.

Diameter of the circle is defined as the distance across the circle. The length of any chord passing through the center is called the diameter of the circle. It is twice the radius.

i.e. diameter = 2 * radius

In the figure, O is the center of the circle, OP is the radius and PQ is the diameter of the circle.

**Circumference of the Circle**

The distance around the outside of the circle is called the circumference of the circle.

Let r be the radius of the circle.

Now, circumference of the circle = 2πr

The value of π is approximately 22/7 or 3.14.

**Area of Circle**

Let r be the radius of circle.

Now, area of circle = π * (radius)^{2} = π * r^{2 }= πr^{2}

The value of π is approximately 22/7 or 3.14.

**Problem: Find the circumference of the circles with the following radius: (Take π = 22/7)**

**(a) 14 cm (b) 28 mm (c) 21 cm**

**Solution:**

(a) Circumference of the circle = 2πr = 2 * 22/7 * 14 = 2 * 22 * 2 = 88 cm

(b) Circumference of the circle = 2πr = 2 * 22/7 * 28 = 2 * 22 * 4 = 176 cm

(c) Circumference of the circle = 2πr = 2 * 22/7 * 21 = 2 * 22 * 3 = 132 cm

**Problem: Find the area of the following circles, given that: (Take π = 22/7)**

**(a) radius = 14 mm (b) diameter = 49 m (c) radius = 5 cm**

**Solution:**

(a) Area of circle = πr^{2} = π * r * r = 22/7 * 14 * 14 = 22 * 14 * 7 = 616 mm^{2}

(b) Diameter = 49 m

So, radius = 49/2 = 24.5 m

Area of circle = πr^{2} = π * r * r = 22/7 * 24.5 * 24.5 = 22 * 24.5 * 3.5

= 616 = 1886.5 m^{2}

(c) Area of circle = πr^{2} = π * r * r = 22/7 * 5 * 5

= (22 * 25)/7 = 550/7mm^{2}

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