Question

12
The diameter of a circle was
12
12 cm and the diameter of the final circle was
9.6
9.6 cm. What is the scale factor? Click Here for Help Video

Answer 1

To find the scale factor between two circles based on their diameters, you can use the formula:

\[
\text{Scale Factor} = \frac{\text{Diameter of Final Circle}}{\text{Diameter of Original Circle}}
\]

In this case, the diameter of the original circle is 12 cm, and the diameter of the final circle is 9.6 cm. Plugging in these values gives:

\[
\text{Scale Factor} = \frac{9.6 \text{ cm}}{12 \text{ cm}} = \frac{9.6}{12}
\]

Now, simplify the fraction:

\[
\text{Scale Factor} = \frac{4 \times 9.6}{4 \times 12} = \frac{9.6 \div 4}{12 \div 4} = \frac{2.4}{3} = \frac{2.4 \div 0.6}{3 \div 0.6} = \frac{4}{5}
\]

Thus, the scale factor is:

\[
\text{Scale Factor} = \frac{4}{5} \text{ or } 0.8
\]

So, the scale factor is **0.8**.