Finding the circumference of a circle

• Mathematics
• Lower Secondary (Key Stage 3)

“Without mathematics, there's nothing you can do. Everything around you is mathematics. Everything around you is numbers.”
Do you agree with this quote? Why?

Circle

The parts of a circle are the radius, diameter, circumference, arc, chord, secant, tangent, sector and segment. A round plane figure whose boundary consists of points equidistant from a fixed point.

What is the numerical equivalent of Pi?

Pi

3.14

What is the circumference of a circle?

1. A line segment going from one point of the circumference to another but does not go through the centre.
2. The distance across the circle going through the centre.
3. The distance from the centre of a circle to the outside.
4. The distance once around the circle.

Finding the circumference of a circle using the radius

What is the radius of a circle?

1. A line segment going from one point of the circumference to another but does not go through the centre.
2. The distance across the circle going through the centre.
3. The distance from the centre of a circle to the outside.
4. The distance once around the circle.

Using the radius

Use the formula C = 2πr to find the circumference using the radius. In this formula, "r" represents the radius of the circle. Again, you can plug π into your calculator to get its numeral value, which is a closer approximation of 3.14.

A radius is any line segment that extends from the center of the circle and has its other endpoint on the edge of the circle.

You might notice this is similar to the C = πd formula. That’s because the radius is half as long as the diameter, so the diameter can be thought of as 2r.

Example

What is the circumference of a circle that has a radius of 6cm?

Answer

37.7cm

Finding the circumference of a circle using the diameter

What is the diameter of a circle?

1. A line segment going from one point of the circumference to another but does not go through the centre.
2. The distance across the circle going through the centre.
3. The distance from the centre of a circle to the outside.
4. The distance once around the circle.

Using the diameter

Use the formula C = πd to find the circumference if you know the diameter. In this equation, "C" represents the circumference of the circle, and "d" represents its diameter. 

That is to say, you can find the circumference of a circle just by multiplying the diameter by pi. Plugging π into your calculator will give you its numerical value, which is a closer approximation of 3.14 or 22/7.

Diameter means a straight line segment that passes through the center of the circle and has its endpoints on the sides of the circle.

Example

What is the circumference of a circle that has a diameter of 9cm?

Answer

28.8cm

Are people born with a specific personality, or is the character the result of their circumstances?

Activities

Parts of a circle

Finding the circumference using the radius and diameter

Using Pi to problem solve

Finding the area using the radius (and diameter)

Finding the area of a circle using the radius (and diameter)

What is the area of a circle?

1. A line segment going from one point of the circumference to another but does not go through the centre.
2. The space inside a 2D shape.
3. The distance from the centre of a circle to the outside.
4. The distance once around the circle.

Finding the area

Square the radius. The formula to find the area of a circle is 2

A=pi r2, where the r variable represents the radius. This variable is squared.

Do not get confused and square the entire equation.

For the sample circle with radius,  r = 6 then r2 (squared) = 36

Using the diameter...

What do you think we do?

What is the area of a circle with a radius of 4cm?

Answer

50.27cm (squared)

Activities

Finding the circumference using the radius and diameter

Finding the area using the radius (and diameter)

Finding the area of a circle GCSE questions

What is success?

Finding the radius of a circle using the circumference.

What is the radius of a circle?

1. A line segment going from one point of the circumference to another but does not go through the centre.
2. The distance across the circle going through the centre.
3. The distance from the centre of a circle to the outside.
4. The distance once around the circle.

Using the circumference

Write down the circumference formula. The formula is C=2\pi r, where C equals the circle’s circumference, and r equals its radii

The symbol pi ("pi") is a special number, roughly equal to 3.14. You can either use that estimate (3.14) in calculations, or use the 

pi symbol on a calculator.

What is the radius of a circle with a circumference of 20m

Answer

3.2m

Finding the circumference of a circle using the area.

What is the area of a circle?

1. The space inside a 2D shape.
2. The distance across the circle going through the centre.
3. The distance from the centre of a circle to the outside.
4. The distance once around the circle.

Find the circumference of a circle with an area of 22cm

Answer

16.6cm

Practice Problems to Calculate Radius of a Circle

1. Circumference of 36π, find circle's radius.

2. Diameter is 12, what is the radius?

3. Circle's area of 113 sq units, find radius.

4. Circle's circumference of 75.4, find radius.

5. Circle's diameter of 20, determine radius.

6. Circumference of 24π, find circle's radius.

7. Circle's area of 153.94 sq units, find radius.

8. Diameter of 14, determine circle's radius.

9. Circle's circumference of 47.12, find radius.

10. Circle's area of 132 sq units, find radius.

Answer key:

1. The radius would be 18.

2. The radius would be 6.

3. The radius would be approximately 3.87298.

4. The radius would be approximately 5.

5. The radius would be 10.

6. The radius would be 4.

7. The radius would be approximately 5.5.

8. The radius would be 7.

9. The radius would be approximately 4.5.

10. The radius would be approximately 6.63324.

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