The answer is 11.25 mm.
A diameter of a circle is twice of its radius: d = 2r ⇒ r = d/2
small circle large circle
radius: r1 radius: r2 = ?
diameter: d1 = 15 mm
⇒ r1 = d1/2 = 15/2 mm
Since the ratio of the radii of two circles is 2:3, we have:
r1 : r2 = 2 : 3
which can also be expressed as:
[tex] \frac{r1}{r2}= \frac{2}{3} [/tex]
We know that r1 is 7.5, so let's implement it:
[tex] \frac{7.5}{r2} = \frac{2}{3} [/tex]
Let's multiply both sides of the by 3r2:
[tex]3r2* \frac{7.5}{r2} =3r2* \frac{2}{3} [/tex]
⇒ [tex]3 * 7.5 = 2*r2[/tex]
[tex]22.5 = 2*r2[/tex]
⇒ [tex]r2= \frac{22.5}{2} =11.25 mm[/tex]
