Question

11. If the ratio of the radii of two circles is 2 : 3, then the ratio of their circumferences is
(a) 2:3
(b) 3:2
(c) 4:9
(d) 9:4​

Answer 1

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If the ratio of the radii of two circles is 2 : 3, then the ratio of their circumferences is:-

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Let the radius of two circle be 2x and 3x respectively. Ratio of Circumference of two circles ; Hence, ratio of their Circumferences is 2 : 3. Thanks for the question !

Syestem solved.

Answer is:-

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Answer 2

Answer :

• The ratio of the circumference of the two circles is 2 : 3

Given :

• Ratio of the radius of the two Circles = 2 : 3

To find :

• Ratio of the circumference of the Circles.

Knowledge required :

• Formula for Circumference of a circle :

⠀⠀⠀⠀⠀⠀⠀⠀⠀C = 2πr

Where :

• C = Circumference of the circle
• r = radius of the circle
• π = 22/7

Solution :

Consider a circle with Radius as r1 and another circle with Radius as r2 .

Now we can find the circumference of both the circles in terms of radius.

Circumference of the first circle :

By using the formula for circumference of a circle and substituting the values in it, we get :

==> C1 = 2πr

==> C1 = 2 × 22/7 × r1

==> C1 = 44r1/7

∴ C1 = 44r1/7

Hence the circumference of the first circle is 44r1/7.

Circumference of the second circle :

By using the formula for circumference of a circle and substituting the values in it, we get :

==> C2 = 2πr

==> C2 = 2 × 22/7 × r2

==> C2 = 44r2/7

∴ C2 = 44r2/7

Hence the circumference of the second circle is 44r2/7.

Ratio of the circumference of the two circle :

==> C1 : C2

By substituting the value of C1 and C2 in the equation , we get :

==> C1 : C2 = 44r1/7 : 44r2/7 ⠀⠀⠀⠀⠀⠀⠀⠀⠀Eq.(i)

Hence the ratio of the two circles is 44r1/7 : 44r2/7.

Now given that the ratio of the radius of the two circles is 2 : 3

So, let's take the radius of the first Circe be 2x and the radius of the second circle be 3x.

Here ,

• r1 = 2x
• r2 = 3x

By substituting the value of r1 and r2 in the equation.(i) , we get :

==> C1 : C2 = 44r1/7 : 44r2/7

==> C1 : C2 = 44/7r1 × 7/44 : r2

==> C1 : C2 = r1 : r2

==> C1 : C2 = 2x : 3x

==> C1 : C2 = 2 : 3

∴ C1 : C2 = 2 : 3

Therefore,

• The ratio of the circumference of the two circles is 2 : 3.