Diameter

Introduction of Diameter

Diameter is an important concept in geometry that helps us better understand circles. The word 'diameter' comes from the Greek word diametros, which means 'across measure'. It is the longest straight line that can be drawn inside a circle, passes through the centre, and touches two points on the boundary.

The diameter is always twice the radius of the circle. This means that if we know the radius, we can easily calculate the diameter using the formula diameter = 2 × radius. Since it is the longest chord of a circle, the diameter is useful to find other circle-related measures, such as circumference and area.

In our daily life, we can see the concept of diameter in many round objects such as coins, plates, bangles, and wheels. Diameter is usually represented by the symbol 'd'. In this article, we will explore its properties, formulas, and relationship with the radius along with sample problems and step-by-step solutions.

 

Table of Contents

• Diameter Formula
• Properties
• Relation between Radius and Diameter
• Fun Facts
• Solved Examples
• Conclusion
• FAQs on Diameter

 

Diameter Formula

The diameter of a circle is a straight line that passes through the centre of the circle and touches the boundary at 2 opposite points.

When we draw the diameter, it divides the circle into 2 equal halves. Each half of the circle is called a semicircle.

The centre of the circle is exactly in the middle of the diameter. This means the diameter is made up of 2 radii joined together. In simple words, the radius is half the diameter, and the diameter is twice the radius.

Diameter (d) = 2 × Radius (r)

Examples of the diameter formula 

1. If the radius of a circle is 5 cm, then

d = 2 × 5 = 10 cm

2. If the  radius of a circle is 7 m, then 

d = 2 × 7 = 14 m 

3. If the radius of a circle is 12 mm, then

d = 2 × 12 = 24 mm 

 

Properties of Diameter

 

Relation between Radius and Diameter

The radius of a circle is the line from the centre to the boundary of the circle. The diameter is a line that goes across the entire circle, passes through the centre and touches the circle at two points.

From this, we can see that a diameter is made of 2 radii. So the relation is:

• Diameter (d) = 2 × radius (r)

• Radius (s) = diameter (d) / 2

This simple relationship helps us solve many problems with circuits.

Formulas using Diameter

We often use the diameter in formulas for the circumference and area of a circle.

• Circumference of a Circle:

We know, 

Circumference = 2πr

Since r = d/2

Circumference = πd

• Area of a Circle:

We know,

Area = πr² 

Since r = d/2,

Area = π( d²)/ 4

 

Fun Facts

• The word "diameter" comes from Greek and means "across measure".

• Wheel spokes usually go through the diameter to keep the wheel strong.

• In old times, people used diameters to draw semicircles and right angles.

• A bigger wheel diameter helps vehicles go faster, but changes the turning power.

• Telescopes with large diameters can collect more light to see faraway stars.

 

Solved Examples

Example 1: The radius of a circle is 6 cm. Find its diameter.

Solution: We know,

Diameter = 2 × Radius

Diameter = 2 × 6

Diameter = 12 cm

 

Example 2: The diameter of a circle is 14 cm. Find its radius.

Solution: We know,

Radius = Diameter / 2

Radius = 14 / 2

Radius = 7 cm

 

Example 3: The radius of a circle is 7 cm. Find its diameter and circumference (take pi = 3.14).

Solution: 

Radius = 7 cm

Diameter = 2 × r = 2 × 7 = 14 cm

Circumference = πd = 3.14 × 14 = 43.96 cm

 

Example 4: The diameter of a circle is 10 cm. Find its area.

Solution: 

Diameter = 10 cm

Radius = d / 2 = 10 / 2 = 5 cm

Area = πr² = 3.14 × 5 × 5 = 78.5 cm² 

 

Example 5: The radius of a circle is 8 cm. Find its diameter and area.

Solution:

Radius  = 8 cm

Diameter = 2r = 2 × 8 = 16 cm 

Area = pi r² = 3.14 × 8 × 8 = 200.96 cm² 

 

Example 6: The area of a circle is 154 cm². Find its diameter and circumference.

Solution:

• Area = 154 cm²

• We know, A = πr²

• 154 = 3.14 × r²

• r² = 49 -> r = 7 cm 

• Diameter = 2r = 14 cm

• Circumference = πd = 3.14 × 14 = 44 cm

 

Conclusion

The diameter is the longest line in a circle, which passes through the centre and divides it into two equal parts. It always doubles the radius and helps find the circle's area and circumference. We see diameter in many real-life objects, such as wheels and coins. Understanding this simple concept makes it very easy to solve circle problems.

 

Frequently Asked Questions on Diameter

1. What are the diameter and radius?

Answer: The radius is the distance from the centre of the circle to any point on its boundary. The diameter is a line that crosses the entire circle, passes through the centre and touches the boundary at two opposite points.

 

2. What is the diameter of a circle?

Answer: The diameter of a circle is the longest straight line inside the circle passing through the centre.

 

3. Is the diameter 2 times the radius?

Answer: The diameter is always 2 times the radius.

Formula: Diameter = 2 × radius

 

4. How many radii are in a circle?

Answer: A circle contains many radii (plural). You can draw a radius from the centre to the boundary in all directions. But a diameter is always made of exactly 2 radii.

 

5. Which one is half: diameter or radius?

Answer: The radius is half the diameter.

Formula: Radius = Diameter / 2