Question

The ratio of circumferences of two circles is 5:3. What is the ratio of their radii ?
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Answer 1

Answer:

5:3

Step-by-step explanation:

Since it's given that the ratio of the circumferences of two circles is 5:3 or 5/3, then we can write the following proportion:

(1.) C₁/C₂ = 5/3, where C₁ is the circumference of one of the circles (the larger one), and C₂ is the circumference of the other circle.

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

C =πr, where π is a universal, well-known constant. Therefore, the two circumferences C₁ and C₂ are each given by one of the following formulas:

(2.) C₁ = πr₁ and C₂ = πr₂, where r₁ and r₂ are the respective radii for each of the two circles.

Now, making the appropriate substitutions from the right sides of equations (2.) into equation (1.) for C₁ and C₂, we have:

(πr₁)/(πr₂) = 5/3

Now, on the left, cancelling out the π's and then simplifying, we have:

[(π)/(π)][(r₁)/(r₂)] = 5/3

[1][(r₁)/(r₂)] = 5/3

r₁/r₂ = 5/3

So, as it can be seen, if the ratio of the circumferences of two circles is 5:3, then the ratio of the radii of the two circles is also 5:3.

Answer 2

Step-by-step explanation:

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