Question

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

Answer 1

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

Answer 2

The scale factor is
`(y)/(z)`

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 =
`(yx)/(2)`

let, Radius of 2nd circle =
`(zx)/(2)`

So, The scale factor =
`(Radius\: of\: 1st\: circle)/(Radius\: of\: 2nd\: circle)`

=
`((yx)/(2))/((zx)/(2))`

=
`(yx)/(2)*(2)/(zx)`

=
`(y)/(z)`

Therefore, The scale factor is
`(y)/(z)`