Question

The ratio of the radii of two circles is 3 : 2. What is the ratio of their circumferences?

Answer 1

We have, the ratio of the radii = 3:2
So, let the radii of the two circles be 3r and 2r, respectively.
Let C₁ and C₂ be the circumferences of the two circles of radii 3r and 2r, respectively. Then,
C₁= 2$\mathrm{\pi }$x 3r = 6$\mathrm{\pi }$r, and C₂ = ​2$\mathrm{\pi }$x2r = 4$\mathrm{\pi }$r
∴
$\frac{C_1}{C_2}=\frac{6\mathrm{\pi }r}{4\mathrm{\pi }r}=\frac{6}{4}=\frac{3}{2}$, or

C₁: C₂ = 3:2.