Question

if the radius of a smaller circle is $r_1 = 6$ and it is dilated to a larger circle with radius $r_2 = 24$, what is the scale factor ($k$)?
a 4
b 2
c 3
d 6

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ for a dilation of two similar figures (in this case, circles) is given by $k=\frac{\text{radius of larger circle}}{\text{radius of smaller circle}}$.

Step2: Substitute given values

We have $r_1 = 6$ (radius of smaller circle) and $r_2=24$ (radius of larger circle). So, $k=\frac{r_2}{r_1}=\frac{24}{6}$.

Step3: Calculate the value of $k$

$\frac{24}{6}=4$.

Answer:

A. 4