The ratio of the radii of two circles is 2: 3. the diameter of the smaller circle is 15 mm. what is the length of the diameter of the larger circle?

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:


We know that r1 is 7.5, so let's implement it:


Let's multiply both sides of the by 3r2:

⇒ 
     
⇒ 

1. 8 or -82. 14 or -143. -11, -3, 0, 7, 10