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

Answer:

the answer is c 22.50

Step-by-step explanation:

i just took the test on ed and got it right

Answer 2

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:
$\frac{r1}{r2}= \frac{2}{3}$

We know that r1 is 7.5, so let's implement it:
$\frac{7.5}{r2} = \frac{2}{3}$

Let's multiply both sides of the by 3r2:
$3r2* \frac{7.5}{r2} =3r2* \frac{2}{3}$
⇒ $3 * 7.5 = 2*r2$
     $22.5 = 2*r2$
⇒ $r2= \frac{22.5}{2} =11.25 mm$