Verified Answer :

chowchow4now

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:

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 \(\frac{y}{z}\)

Related Questions