Answered

The "Super Size" cup is 1.5 times larger than the "Large"-size cup across all
dimensions. (In other words
, the cups are similar figures with a linear scale
factor of 1.5.) If
a "Large" soda cup holds 20 ounces of soda, how many
ounces of soda would a "Super Size" cup hold?

Verified Answer :

GinnyAnswer

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

\(\[ \text{Volume scale factor} = 1.5^3 = 3.375 \]\)

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

\(\[ \text{Volume of the "Super Size" cup} = 20 \text{ ounces} \times 3.375 = 67.5 \text{ ounces} \]\)

Hence, a "Super Size" cup holds 67.5 ounces of soda.

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