Question

If the ratio of the radius of two circles is 3:4 , then the ratio of their circumfrence is​

Answer 1

Answer:

Since it's given that the ratio of the radii of two circles is 3:4 or 3/4, then we can write the following proportion:

(1.) r₁/r₂ = 3/4, where r₁ is the radius of one of the circles (the smaller one), and r₂ is the radius of the other circle.

We know that the relationship between the radius r of a circle and the area A of a circle is given by the following formula:

A =πr², where π is a universal, well-known constant. Therefore, the two areas A₁ and A₂ are each given by one of the following formulas:

(2.) A₁ = π(r₁²) and A₂ = π(r₂²)

Now, ratio of the areas of the two circles is:

A₁/A₂ = [π(r₁²)]/[π(r₂²)]

= (π/π)[(r₁²)/(r₂²)]

= (π/π)[(r₁/r₂)²]

Substituting on the right from equation (1.), we have:

= (π/π)[(3/4)²]

= (1)(3/4)²

= (3/4)²

= (3/4)(3/4)

A₁/A₂ = 9/16

So, as it can be seen, if the ratio of the radii of two circles is 3:4, then the ratio of the areas of the same two circles is 9:16.