What is the Diameter Formula?

Diameter is defined as the line that divides the circle into 2 halves i.e., each part is known as a semicircle. The center of the circle act as the midpoint of diameter. This means that it divides the diameter into 2 halves and each part is noted as a radius.

Circle

From the above figure, r represents the radius of the circle and D represents the diameter of the circle. 

Diameter of circle

The distance from the centre of the circle to any point on its boundary is the same and that is known as radius. Diameter is known as the longest chord. Whereas chord is defined as the line segment that joins the 2 sides of a circle.

D = 2 × R

Where R is the radius of the circle

The enclosing boundary of the circle is known as the circumference. Diameter is expressed in terms of circumference as,

C = 2 × π × R

Where C is the circumference of the circle

Earlier when scientists were finding the relation between radius, circumference and diameter, they found that their ratio is constant for every circle and that is π, which is an irrational number and holds a value 3.14 or 22/7.

D = 2 × R 

C = D × π 

Diameter of circle

D = C / π 

Sample Problems

Question 1: Find the diameter of a circle having a radius of 6 cm.

Solution:

Given the radius of the circle as R = 6cm.

Diameter of a circle is given by  D = 2 × R

D = 2 × 6 cm 

D =12 cm.

Question 2: Find the diameter of a circle having a radius of 39 cm.

Solution:

Given the radius of the circle as R = 39cm.

Diameter of a circle is given by D = 2 × R

D = 2 × 39 cm.

D = 78 cm.

Question 3: Find the diameter of a circle having a circumference of 20 cm.

Solution:

Given circumference of circle C = 20 cm.

Diameter of a circle in terms of circumference is given by D = C / π

D = 20 / π 

= 20 / 3.14

= 6.369426751cm

Question 4: Find the diameter of a circle having a circumference of 2π cm.

Solution:

Given circumference of circle C = 2π cm.

The diameter of a circle in terms of the circumference is given by D = C / π

D = 2 π / π

= 2cm

Question 5: Find the diameter of a circle having a circumference of 44 cm.

Solution:

Given circumference of circle C = 44 cm.

Diameter of a circle in terms of circumference is given by D = C / π

D = 44 / π

π = 22/7

= 44 / (22/7)

= (44 × 7) / 22

= 14cm

Question 6: Find the diameter of a circle having a radius of √20cm.

Solution:

Given the radius of the circle as R = √20cm.

Diameter of a circle is given by  D = 2 × R

D = 2 × √20

D = 2√20 cm.

Question 7: Find the diameter of a circle having a radius of 9π cm.

Solution:

Given the radius of the circle as R = 9π cm.

The diameter of a circle is given by D = 2 × R

D = 2 × 9π

D = 18π cm.