A prism with a volume of \( 1458 \mathrm{~mm}^{3} \) is scaled down to a volume of \( 16 \mathrm{~mm}^{3} \). What is the scale factor? \( \frac{8}{729} \) \( \frac{2}{27} \) \( \frac{8}{9} \)

To find the scale factor, we need to determine the ratio of the volumes of the two prisms. Given: - Volume of the original prism = \( 1458 \, \text{mm}^3 \) - Volume of the scaled-down prism = \( 16 \, \text{mm}^3 \) The scale factor is the ratio of the volumes of the two prisms. Let's denote the scale factor as \( S \). The volume of the original prism is \( 1458 \, \text{mm}^3 \) and the volume of the scaled-down prism is \( 16 \, \text{mm}^3 \). The scale factor \( S \) can be calculated using the formula: \[ S = \frac{\text{Volume of the scaled-down prism}}{\text{Volume of the original prism}} \] Substitute the given values: \[ S = \frac{16}{1458} \] Now, we can calculate the scale factor. Calculate the value by following steps: - step0: Calculate: \(\frac{16}{1458}\) - step1: Reduce the fraction: \(\frac{8}{729}\) The scale factor is \( \frac{8}{729} \).