# The ratio of the circumference of two circles is 3/2. The radius of the smaller circle is 8 inches. What is the radius of the larger circle?

Nov 14, 2016

The circumference is given by $2 \pi r$.

$C = 2 \pi r$

$C = 2 \pi \left(8\right)$

$C = 16 \pi$

Set up your proportion. Let $C$ be the circumference of the larger circle.

$\frac{16 \pi}{C} = \frac{2}{3}$

$C = \frac{16 \pi \times 3}{2}$

C = 24π" inches"

Solve for r:

$C = 2 \pi r$

24π = 2pir

$r = \frac{24 \pi}{2 \pi}$

$r = 12 \text{ inches}$

Hopefully this helps!