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Perimeter of a Circle

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

 

 

Example 1:

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

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.

 

 

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

 

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.

 

 

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

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

 

 

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

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

 

 


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?

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.

 

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