To determine the factor by which the dimensions of the smaller prism are multiplied to produce the corresponding dimensions of the larger prism, we can follow these steps:
1. Compare the dimensions of the lengths:
Calculate the factor for the length:
[tex]\[
\text{factor\_length} = \frac{14.7 \, \text{cm}}{4.2 \, \text{cm}}
\][/tex]
Using the given values, this fraction simplifies to approximately:
[tex]\[
3.4999999999999996
\][/tex]
2. Compare the dimensions of the widths:
Calculate the factor for the width:
[tex]\[
\text{factor\_width} = \frac{20.3 \, \text{cm}}{5.8 \, \text{cm}}
\][/tex]
Using the given values, this fraction simplifies to approximately:
[tex]\[
3.5000000000000004
\][/tex]
3. Compare the dimensions of the heights:
Calculate the factor for the height:
[tex]\[
\text{factor\_height} = \frac{33.6 \, \text{cm}}{9.6 \, \text{cm}}
\][/tex]
Using the given values, this fraction simplifies to approximately:
[tex]\[
3.5000000000000004
\][/tex]
As the prisms are similar, all the multiplication factors should be the same. Based on our calculations, you can see that the factors for all dimensions are very close to each other and can be considered to be a common factor of:
[tex]\[
3.5
\][/tex]
Thus, the dimensions of the smaller prism are multiplied by a factor of:
[tex]\[
3 \frac{1}{2}
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{3 \frac{1}{2}}
\][/tex]
