Sure, let's walk through solving this question step-by-step.
1. Understanding the Problem:
We have two soda cups, a "Large" soda cup and a "Super Size" cup. The "Super Size" cup is scaled up by a factor of 1.5 in every dimension compared to the "Large" cup. We need to determine how many ounces of soda the "Super Size" cup holds.
2. Given Information:
- The "Large" soda cup holds 20 ounces.
- The "Super Size" cup is 1.5 times larger in each dimension than the "Large" cup.
3. Key Concept – Volume Scaling:
When scaling a three-dimensional object, the volume scales with the cube of the linear scale factor. This is because volume is a three-dimensional measurement.
4. Calculating the Volume Scaling Factor:
- Linear scale factor = 1.5
- Volume scale factor = (linear scale factor)³
[tex]\[
\text{Volume scale factor} = 1.5^3 = 3.375
\][/tex]
5. Calculating the Volume of the "Super Size" Cup:
- Volume of the "Large" soda cup = 20 ounces
- Volume of the "Super Size" cup = Volume of the "Large" soda cup × Volume scale factor
[tex]\[
\text{Volume of the "Super Size" cup} = 20 \text{ ounces} \times 3.375 = 67.5 \text{ ounces}
\][/tex]
Hence, a "Super Size" cup holds 67.5 ounces of soda.
