Question

The ratio of the radii of two circle is 5 : 3. Find the ratio of their circumferences.

Answer 1

Let the radii of the given circles be 5x and 3x, respectively.
Let their circumferences be C₁ and C_2, respectively.

C₁ = $2\times \pi \times 5x=10\mathrm{\pi }x$

C₂ = $2\times \pi \times 3x=6\mathrm{\pi }x$
∴ $\frac{C_1}{C_2}=\frac{10\pi x}{6\pi x}=\frac{5}{3}$
⇒ C₁:C₂ = 5:3
Hence, the ratio of the circumference of the given circle is 5:3.