Question

the area of two circles are in the ratioo 16:25. find the ratio of their circumferences

Answer 1

\[\dfrac{\pi r_1^2}{\pi r_2 ^2} = \dfrac{r_1^2}{r_2^2} = \left(\dfrac{r_1}{r_2}\right)^2 = \dfrac{16}{25}\]You want to know the value of\[\dfrac{2\pi r_1}{2\pi r_2} = \dfrac{r_1}{r_2} \]

Answer 2

That works in general. If the areas of similar shapes are in ratio \(a:b\), then the lengths (any kind of) will be in ratio \(\sqrt{a} : \sqrt{b}\)

Answer 3

Can also extend this fact to volumes, etc.

Answer 4

area of the circle wrt to square is constant

Answer 5

how to rescale a square if u want 16:25 ratio?