Question

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?

Answer 1

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:

`(r1)/(r2)= (2)/(3)`

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

`(7.5)/(r2) = (2)/(3)`

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

`3r2* (7.5)/(r2) =3r2* (2)/(3)`
⇒
`3 * 7.5 = 2*r2`

`22.5 = 2*r2`
⇒
`r2= (22.5)/(2) =11.25 mm`