Perimeter is the distance around a closed figure and is typically measured in millimetres (mm), centimetres (cm), metres (m) and kilometres (km). These units are related as follows:

10 mm = 1 cm

100 cm = 1 m

1000 m = 1 km

The word 'perimeter' is also sometimes used instead of circumference.

If we know the radius

Given the radius of a circle, the circumference or perimeter can be calculated using the formula bwloe:

Perimeter (P) = 2 · π · R

where: R is the radius of the circle π is Pi, approximately 3.142

If we know the diameter

If we know the diameter of a circle, the circumference can be found using the formula

Perimeter (P) = π · D

where: D is the diameter of the circle π is Pi, approximately 3.142

If we know the area

If we know the area of a circle, the circumference can be found using the formula:

Perimeter (P) = √(4 · π · A )

where: A is the area of the circle π is Pi, approximately 3.142

Smart Math Example 1:

A circular flower-bed has a radius of 9 m. Find the perimeter/circumference of the flower-bed.

Smart Solution:

P = 2 · π · R

P = 2 · 3.1416 · 9

P = 56.5487 cm

So, the perimeter/circumference of the flower-bed is 56.5487 m.

Smath Math Example 2: Find the perimeter of the given circle whose diameter is 4.4 cm.

Smart Solution:

Given that:

Diameter of the circle (D) = 4.4 cm.

We know the formula to find the perimeter of the circle if the diameter is given, namely π·D.

Substitute the diameter 4.4 and Pi value as 3.14 in the above formula.

Perimeter = (3.14)(4.4) = 13.82

Therefore 13.82 cm is the perimeter of the given circle.

Smart Math Example 3: If the radius is 11.7 cm. Find perimeters (circumference) of the circle.

Smart Solution:

Given that:

Radius (r) = 11.7cm

Perimeter (circumference) of circle P = 2 π r

Substitute the r value in the formula, we have:

P = 2 x 3.14 x 11.7

P = 79.56 cm

Thus, the perimeter of the circle is 79.56cm

Smart Math Example 4: Find the perimeter and area of the circle, if the radius of the circle is 8cm.

Smart Solution: We have given the radius, which is 8cm. So, by using the formula of the perimeter of the circle, we have:

P = 2πr

P = 2×3.14×8

P = 50.24 cm

And for the area of the circle:-

A = π r2

A = 3.14×(8)2

A = 200.96cm2

Smart Math Example 5: The wheel of a bullock cart has a radius of 6 m. If the wheel rotates once how much distance does the cart move?

Smart Solution:

If the wheel rotates once, the cart will move by a distance equal to the perimeter of the wheel.

Step 1:

P = 2πr

P = 2× 3.14× 6 = 37.68 m

Thus, the bullock cart moves 37.68 m in one revolution of the wheel.

That is Formula Math Perimeter of a Circle