Find the ratio of their circumferences

Question

The areas of two circles are 144 (pie) cm²  and 64 (pie) cm². Find the ratio of their circumferences.

Answer 1

A = ∏r²

C = 2∏r

 

A₁ = 144∏

A₂ = 64∏

 

If we take the square roots of the coefficients, we will get their radiuses:

r₁ = √144 = 12

r₂ = √64 = 8

 

Now we put that into our circumference equation:

C₁ =2 * 12∏ = 24∏

C₂ = 2 * 8∏ = 16∏

 

This gives 24∏:8∏. We can simplify this. 24 and 8 have an 8 in common, and both also have a ∏ in common.

24 / 8 = 3

8 / 8 = 1

∏ / ∏ = 1

 

So we no have:

3*1:8*1, or

3 cm:1 cm