Question

The ratio of the radii of two circles is 3:7.
Calculate ratio of their circumferences.
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Answer 1

Answer:

Let, the radii of each cirlcle be 3x and 7x respectively,

We know, the formula for calculating the area for circle is πr^2.

Therefore, the ratio of the circles, are—

π(3)^2 : π(7)^2

= (3)^2 : (7)^2

= 9:49

Answer 2

Answer :-

• The ratio of circumference is 3/7.

Step-by-step explanation:

To Find :-

• The ratio of circumference

Solution:

Given that,

• The ratio of the two radii of two circles = 3:7

Therefore,

$\underline{\sf{ratio \: of \: to \: radii}} = \sf{\dfrac{3}{7}}$

Assumption:

Let us assume the two radii as 3x and 7x,

Now,

We know that,

• Circumference of circle = 2πr

Therefore, the ratio of circumference with the value of radius :-

$\longrightarrow \: \sf{\dfrac{2 \pi \: 3x}{2 \pi \: 7x}}$

Cancelling 2 from numerator and denominator

$\longrightarrow \: \sf{\dfrac{2 \pi \: 3x}{2 \pi \: 7x}}$

$\longrightarrow \: \sf{\dfrac{\not{2}\pi\: 3x}{\not{2}\pi \: 7x}}$

$\longrightarrow \: \sf{\dfrac{\pi \: 3x}{\pi \: 7x}}$

Cancelling π from numerator and denominator

$\longrightarrow \: \sf{\dfrac{ \not{\pi} \: 3x}{ \not{\pi} \: 7x}}$

$\longrightarrow \: \sf{\dfrac{3x}{7x}}$

Cancelling x from numerator and denominator

$\longrightarrow \: \sf{\dfrac{3}{7}}$

Hence,

The ratio of circumference :-

$\leadsto \: \boxed{\bf{ \red{\dfrac{ \: 3 \:}{ \: 7 \:}}}} \: \bigstar$