Question

The ratio of the diameters of two circles is y:z. What is the scale factor of the circles?

Answer 1

Scale factor is based on the radii of two circles. So each radius for your two circles are y/2 and z/2. The scale factor would just be the ratio of the radii, so it would be $\frac{\frac{y}{2}}{\frac{z}{2}}=\frac{y}{z}$

Answer 2

Answer:

The scale factor is $\frac{y}{z}$

Step-by-step explanation:

Given: Ratio of diameter of 2 circles which is y : z

To find: Scale Factor of the circles

Scale factor of circles is the ratio of their radii.

let, a is the same multiple which given exact value of diameter

⇒ The diameter of 1st circle = ya

⇒ Radius of 1st circle = $\frac{ya}{2}$

⇒ The diameter of 2nd circle = za

⇒ Radius of 2nd circle = $\frac{za}{2}$

So, The scale factor = $\frac{Radius\: of\: 1st\: circle}{Radius\: of\: 2nd\: circle}$

                                 = $\frac{\frac{ya}{2}}{\frac{za}{2}}$

                                 = $\frac{ya}{2}\times\frac{2}{za}}$

                                 = $\frac{y}{z}$

Therefore, The scale factor is $\frac{y}{z}$