Question

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

Answer 1

Answer:

The scale factor is  $\frac{y}{z}$

Step-by-step explanation:

We are Given with Ratio of diameter of 2 circles which is y : z

We have to find  Scale Factor of the circles

• Scale factor of circles is the ratio of their radii.

let, Radius of 1st circle = $\frac{yx}{2}$

let, Radius of 2nd circle = $\frac{zx}{2}$

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

                                 = $\frac{\frac{yx}{2}}{\frac{zx}{2}}$

                                 = $\frac{yx}{2}\times\frac{2}{zx}$

                                 = $\frac{y}{z}$

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

Answer 2

The scale factor is the ratio of the areas of the 2 circles.

areas =  pi (y/2)^2 and pi (z/2)^2

 so required ratio = y^2 : z^2