Circumference of a circle

Circumference of a circle

Concept

A Circle is a round closed figure where all its boundary points are equidistant from a fixed point called the center.
The circumference of a circle is the perimeter of the circle. It is the total length of the boundary of the circle. The circumference of a circle is the product of the constant π and the diameter of the circle. A person walking across a circular park, or a circular table to be bordered requires this metric of the circumference of a circle. The circumference is a linear value and its units are the same as the units of length.

The radius is the distance from the center outwards.
The diameter goes straight across the circle, through the center.
The circumference is the distance once around the circle.

Rules

Radius is half of the diameter. To find the radius divide the diameter by 2.
Radius = \fn_phv \frac{diameter}{2} or r = \fn_phv \frac{d}{2}

The diameter is twice the radius. To find the diameter, multiply the radius by 2.
Diameter = 2 × Radius or d = 2r

To find the circumference, multiply the value of pi (π) with the diameter or multiply the value of pi (π) with the double of the radius.
Circumference = π × Diameter or C = πd
Circumference = 2 x π × Radius or C = 2πr

Example

What is the circumference of the circle below?

Solution

To find the circumference, multiply the value of pi (π) with the diameter.

Circumference = π × Diameter or C = πd

Circumference = π × 14 mm

Circumference = 43.98 mm

Practice Circumference of a circle

Practice Problem 1

What is the circumference of the circle below? Use \fn_phv {\color{Teal} \frac{22}{7}} as pi.
Give your answer as a mixed number or a decimal rounded to the nearest tenth.
Circumference of a circle Problem 1

Practice Problem 2

What is the circumference of the circle below? Use \fn_phv {\color{Teal} \frac{22}{7}} as pi.
Circumference of a circle Problem 2

Practice Problem 3

Emma has made a circular cake and will decorate the top edge with a yellow ribbon. How many meters of ribbon does she need to put around the cake if the diameter of the cake is 0.6 m. Use 3.142 or \fn_phv {\color{Teal} \frac{22}{7}}  for π.
Round the answer to the nearest tenth.
Circumference of a circle Problem 3

The circumference of a circle is the perimeter of the circle. It is the total length of the boundary of the circle.

Circle – the set of all points in a plane that are the same distance from one fixed point.

Center – one point in the middle of a circle that is the same distance from all of the points on the circle.

Diameter – the distance across a circle that passes through the center.

Radius – the distance from the center to any point on the circle.

Pi (π) – the constant that results from dividing the circumference of a circle by its diameter. The value is approximated as 3.142 or \fn_phv \frac{22}{7}.