# 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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