Question

Circumference (c) of a circle is directly proportional to its diameter (d)
Write using the symbol of variation

Answer 1

We know that, 2r = d

Circumference(c) = 2πr
C = 2πr
C = πd

We know that π is a constant
Let suppose take k as constant

C =kd
C∝ d

Answer 2

The circumference (C) of a circle is directly proportional to its diameter (D) may be written as ; $\bf \red{C\propto D}$

Given:

• Circumference (C) of circle.
• Diameter(D) of circle.

To find:

• Using symbols of variation show that, Circumference (C) of a circle is directly proportional to its diameter (D).

Solution:

We know that,

If two variables x and y are proportional to each other,

That means, if x increases then y will also increase and vice versa.

This can be shown as; $x \propto \: y$

Now,

As we know that,

Circumference of circle

$\bf C = 2\pi \: r$

here, r is the radius of the circle.

And we also know that, Diameter = 2 ×radius

or

$\bf D = 2r$

So,

We can write that

$\bf C= \pi \: D$

As, π is a constant, its value is always fixed, i.e 22/7 or

≈ 3.14

That means, if D increases then the value of C will increase and vice-versa.

we can write that $\bf C \propto \: D$

Thus,

Circumference (C) of a circle is directly proportional to its diameter (D) may be written as $\bf C\propto D$

Learn more:

1) y varies directly as square root of x. When x = 16, y = 24. Find the constant of variation and equation of variation.

https://brainly.in/question/4841013

2) x varies directly as y, when x = 5, y = 30. Find the constant of variation and equation of variation.

https://brainly.in/question/4841011

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