To find the scale factor between two similar cylinders based on their volumes, you can use the formula for the ratio of their volumes, which is related to the scale factor by the cube of that scale factor.
Let \( V_1 \) be the volume of the larger cylinder (512) and \( V_2 \) be the volume of the smaller cylinder (64).
We know that:
\[ \text{Ratio of volumes} = \frac{V_2}{V_1} = \frac{64}{512} \]
Calculating this gives:
\[ \frac{64}{512} = \frac{1}{8} \]
The scale factor \( k \) is related to the volumes by the equation:
\[ \frac{V_2}{V_1} = k^3 \]
So we have:
\[ k^3 = \frac{1}{8} \]
To find \( k \), we take the cube root of both sides:
\[ k = \sqrt[3]{\frac{1}{8}} = \frac{1}{2} \]
Thus, the scale factor of the small cylinder to the large cylinder is \( \frac{1}{2} \) or 0.5.
3 answers