Relation between Diameter Radius and Circumference

Relation between diameter radius and circumference are discussed here.

Relation between Diameter and Radius:

Relation between radius and diameter of a circle

In this figure, we have a circle with centre O.

OA is the radius and PQ is the diameter.

Relation between radius OA and diameter PQ.

You will find that.

PQ = 2 OA

Therefore, Diameter = 2 × Radius

In other words, we say diameter is twice the radius.

$Relation between Radius and Diameter of a Circle$

1. What is the relation between diameter and radius?

Solution:

Diameter of a circle is twice of its radius.

Formula:

Diameter = 2 radius

Radius = $\frac{Diameter}{2}$

For Example:

1. Find the diameter of a circle whose radius is 4.5 cm.

Solution:

We know, Diameter = 2 radius.

Radius = 4.5 cm.

= 2 x 4.5 cm.

= 9 cm.

Therefore, diameter = 9 cm.

2. Find the radius of a circle whose diameter is 7 cm.

Solution:

We know, Radius = Diameter/2

Diameter = 7 cm.

= 7/2 cm.

= 3.5 cm.

Therefore, radius = 3.5 cm.

3. Find the diameter of a circle whose radius is 1.5 cm.

Solution:

We know, Diameter = 2 radius.

Radius = 1.5 cm.

= 2 x 1.5 cm.

= 3 cm.

Therefore, diameter = 3 cm.

4. Find the radius of a circle whose diameter is 8 cm.

Solution:

We know, Radius = Diameter/2

Diameter = 8 cm.

= 8/2 cm.

= 4 cm.

Therefore, radius = 4 cm.

5. Find the diameter of a circle whose radius is 2 cm.

Solution:

We know, Diameter = 2 radius.

Radius = 2 cm.

= 2 x 2 cm.

= 4 cm.

Therefore, diameter = 4 cm.

6. If the radius of a circle is 3 cm, find its diameter.

Solution: Diameter = 2 × Radius

= 2 × 3 cm

= 6 cm.

Relation between Circumference and Diameter:

1. What is the relation between circumference and diameter?

Solution:

Circumference of a circle is slightly more than three times of its diameter.

Worksheet on Relation between Diameter Radius and Circumference:

1. Find the radius of the circle whose diameter is:

(i) 10 cm

(ii) 14 cm

(iii) 16 cm

(iv) 8 cm

Answer:

1. (i) 5 cm

(ii) 7 cm

(iii) 8 cm

(iv) 4 cm

2. Find the diameter of the circle whose radius is:

(i) 4 cm

(ii) 6 cm

(iii) 7 cm

(iv) 5 cm

Answer:

2. (i) 8 cm

(ii) 12 cm

(iii) 14 cm

(iv) 10 cm

3. Complete the following table:

Radius

4 cm

____ cm

____ m

6 m

14 mm

Diameter

____ cm

20 cm

6 m

____ m

____ mm

Answer:

Radius

4 cm

10 cm

3 m

6 m

14 mm

Diameter

8 cm

20 cm

6 m

12 m

28 mm

4. Fill in the blanks:

(i) The length of the radius of a circle is _____ the length of its diameter.

(ii) Diameter is also a _____ of the circle.

(iii) The line segment that joins two points on a circle is called a _____ of the circle.

(iv) The distance around a circle is called its _____.

(v) A diameter of a circle passes through the _____ of the circle.

Answer:

4. (i) half

(ii) chord

(iii) chord

(iv) circumference

(v) center

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