1. What is a circle?
A circle is a round 2D shape which has no sides or corners.
1.1 Radius and diameter of circles
Radius: It is the distance from the centre of the circle to any point on its edge(boundary of the circle).
For the circle shown above, O is the centre of the circle and point A is on the edge.
OA is the radius of the circle.
Diameter: The diameter is the distance across the middle of the circle.
For the circle shown above, AB is the line passing through the centre O.
AB is the diameter of the circle.
Note: The diameter of a circle is twice the radius.
1.2 Solved example
Work out the radius of the circle whose diameter is 15 cm.
Solution: Given the diameter of the circle d = 15 cm
Let the radius of the circle be r.
Diameter is twice the radius.
d = 2 × r
r = d ÷ 2
r = 15 ÷ 2
r = 7.5 cm
Radius of the circle is 7.5 cm.
2. Circumference and area of a circle
Circumference: It is the distance around the circle. For example, if you take a wire of length 5 cm and bend it to form a circle, the circumference of the circle formed is the total length of the wire which is 5 cm.
To calculate the circumference of a circle, all we need to know is the radius of the circle and remember the formula, which is:
Circumference of the circle = 2 × π × r
For the formula use π = 3.14 or π = 22/7
Area: It is the total region covered inside the boundary of a circle, and is measured in square units.
To calculate the circumference of a circle, all we need to know is the radius of the circle and remember the formula, which is:
Area of Circle = π × (r)²
2.1 Solved Example
Amber got a frisbee as a birthday present. The diameter of the frisbee is 28 cm.
Find the circumference and area of the frisbee. Use π = 22/7
Solution:
Diameter is twice the radius, so
Radius of frisbee = 28÷2 = 14 cm
Circumference of frisbee = 2 × π × r
= 2 × 22⁄7 ×14
= 44 × 2
= 88 cm
Area of frisbee = π × (radius)²
= 22⁄7 × 14²
= 22⁄7 × 196
= 616 cm²
3. Semicircles
Semicircles are simply half of a circle. If you divide a circle into two exact parts, then each part is called a semicircle.
Circumference of a semicircle is the total length along its boundary, which is the sum of half the circumference of the circle and twice its radius.
Circumference of semicircle = Half of circumference of circle + 2 × r
= 1⁄2 × 2 × π × r +2 × r
= π × r + 2 × r
Area of semicircle = Half of the area of the circle
= 1⁄2 × π × (r)²
3.1 Solved example
Work out the circumference and area of the shape shown below. Use π=22⁄7
Solution: The shape shown above is a semicircle of radius 21 cm.
So r = 21 cm
Circumference of the shape = π × r +2 × r
= 22⁄7 × 21 +2 × 21
= 66+42
= 108 cm
Area of the shape = 1⁄2 × π × (r)²
= 1⁄2 × 22⁄7 × (21)²
= 693 cm²
