To determine the factor by which each dimension of the smaller prism has been multiplied to obtain the dimensions of the larger prism, follow these steps:
1. Identify the dimensions of both prisms:
- Smaller prism: length \(4.2 \text{ cm}\), width \(5.8 \text{ cm}\), height \(9.6 \text{ cm}\).
- Larger prism: length \(14.7 \text{ cm}\), width \(20.3 \text{ cm}\), height \(33.6 \text{ cm}\).
2. Calculate the multiplication factor for each dimension by dividing the dimensions of the larger prism by the corresponding dimensions of the smaller prism:
- Factor for the length:
[tex]\[
\text{Factor}_{\text{length}} = \frac{14.7 \text{ cm}}{4.2 \text{ cm}} = 3.5
\][/tex]
- Factor for the width:
[tex]\[
\text{Factor}_{\text{width}} = \frac{20.3 \text{ cm}}{5.8 \text{ cm}} = 3.5
\][/tex]
- Factor for the height:
[tex]\[
\text{Factor}_{\text{height}} = \frac{33.6 \text{ cm}}{9.6 \text{ cm}} = 3.5
\][/tex]
3. Verify that the factors are consistent across all dimensions:
Each multiplication factor calculated (length, width, height) results in a factor of approximately \(3.5\).
4. Conclude the common factor:
Since the common factor for multiplying each dimension of the smaller prism to get the corresponding dimension of the larger prism is consistent and equal to \(3.5\), the answer is:
[tex]\[
3.5 = 3 \frac{1}{2}
\][/tex]
Thus, each dimension of the smaller prism is multiplied by [tex]\(3 \frac{1}{2}\)[/tex] to produce the corresponding dimensions of the larger prism.
