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 determine the scale factor between the two volumes of the prism, we can use the formula relating the volumes of similar three-dimensional figures. The volume of the smaller prism is given by \( V_{\text{small}} = k^3 \times V_{\text{large}} \), where \( k \) is the scale factor. Thus: \[ k^3 = \frac{V_{\text{small}}}{V_{\text{large}}} = \frac{16 \, \text{mm}^3}{1458 \, \text{mm}^3} \] Calculating this gives: \[ k^3 = \frac{16}{1458} = \frac{8}{729} \] To find \( k \), take the cube root: \[ k = \sqrt[3]{\frac{8}{729}} = \frac{2}{9} \] So, the scale factor is \( \frac{2}{9} \), which is not given in your options. However, this seems to be the method to calculate it. Please ensure the values provided match the expected answers.