Question

1. what scale factor should be applied to a solid to produce a volume that is four times as large as the original volume?

4
1.59
1.12
64

Explanation:

Step1: Recall Volume Scale Factor Relationship

For similar solids, if the linear scale factor is \( k \), the volume scale factor is \( k^3 \). Let the original volume be \( V \) and the new volume be \( 4V \). So we have \( k^3=\frac{\text{New Volume}}{\text{Original Volume}} = 4 \).

Step2: Solve for \( k \)

To find \( k \), take the cube root of 4. \( k=\sqrt[3]{4}\). Calculate \( \sqrt[3]{4}\approx1.59 \) (since \( 1.59^3\approx1.59\times1.59\times1.59\approx2.5281\times1.59\approx4 \)).

Answer:

1.59 (the option with 1.59)