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The perimeter of a circle and its diameter vary _______ with each other.

Solution:

The perimeter(P) of a circle of radius ‘r’

P = 2πr

Diameter of a circle is twice the radius, therefore

Diameter (D) = 2r

Therefore Perimeter(P) = πD

The ratio of perimeter and diameter is

P/D = πD/D = π

The ratio of perimeter to diameter is the constant π, therefore

Perimeter of the circle and the diameter are directly proportional.

✦ Try This: The Area of the circle and the perimeter of the circle are directly proportional to each other. Is the statement true or false?

Let us assume a circle of radius r

The Perimeter(P) of the circle = 2πr

The Area(A) of the circle = πr²

The ratio of the Area of the circle and Perimeter of the circle is :

A/P = πr²/2πr = r/2

Now the ratio r/2 is not a constant, hence

The Area of the circle and diameter of the circle are not directly proportional.

The table below also proves the same:

Radius(r)	1	2	3	4	5
Area(A)	π	4π	9π	16π	25π
Perimeter(P)	2π	4π	6π	8π	10π
Ratio(A/P)	1/2	1	3/2	2	5/2

Since the ratio A/P is varying and not constant we can again conclude that the area of the triangle and the perimeter of the triangle are not directly proportional.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 13

NCERT Exemplar Class 8 Maths Chapter 10 Problem 33

The perimeter of a circle and its diameter vary _______ with each other.

Summary:

The perimeter of a circle and its diameter vary directly with each other.

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