Question

if the ratio of the areas of two circle is 4:25 then the ratio of their circumference is ?​

Answer 1

Answer:

Let the radius of two circles be r₁ and r₂

Then, according to question

πr₁² / πr₂² = 4/25

r₁ / r₂ = 2/5

Now,

Ratio of circumference = 2 π r₁ / 2 π r₂

= r₁ / r₂

= 2 / 5

∴ Ratio of their circumference is 2 : 5

Step-by-step explanation:

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Answer 2

Given : The ratio of the areas of two circle is 4:25

To find : The ratio of their circumference.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the required ratio)

Let,

The radius of the first circle = x

and, the radius of the second circle = y

Now, area of a circle = π × (radius)²

So,

• Area of first circle = π × x²
• Area of the second circle = π × y²

According to the data mentioned in the question,

$\pi {x}^{2} :\pi {y}^{2} = 4:25$

$\frac{\pi {x}^{2} }{\pi {y}^{2} } = \frac{4}{25}$

$\frac{ {x}^{2} }{ {y}^{2} } = \frac{4}{25}$

$\frac{x}{y} = \frac{2}{5}$

$x : y = 2 : 5$

Now, circumference of a circle = 2 × π × radius

So,

• Circumference of the first circle = ( 2 × π × x )
• Circumference of the second circle = (2 × π × y)

Now, the ratio of their circumference :

$= ( 2 × π × x ) : ( 2 × π × y )$

$= \frac{( 2 × π × x )}{( 2 × π × y )}$

$= \frac{x}{y}$

$= x : y$

$= 2 : 5$

(This will be considered as the final result.)

Hence, the ratio of their circumference is 2:5