5th Grade Monuments and Landmarks - Free Printable

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Problem: The Statue of Liberty

Task:
The Statue of Liberty is 151 feet tall from the base of the pedestal to the tip of the torch. A scale model of the statue is being made that is 18 inches tall. You are to find the scale factor of the model to the actual statue.

Instructions:
- You are to write a proportion.
- Use the ratio of the height of the model to the height of the real statue.
- Then, use cross multiplication to solve for the unknown.

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Step-by-Step Solution:

We are given:
- Height of actual Statue of Liberty = 151 feet
- Height of model = 18 inches

But we need both measurements in the same units. Let's convert feet to inches since the model is measured in inches.

> 1 foot = 12 inches
> So, 151 feet = 151 × 12 = 1,812 inches

Now:
- Actual height = 1,812 inches
- Model height = 18 inches

We want to find the scale factor (model : actual), which is:

$$
\frac{\text{Model height}}{\text{Actual height}} = \frac{18}{1812}
$$

Simplify this fraction:

Divide numerator and denominator by 6:

$$
\frac{18 ÷ 6}{1812 ÷ 6} = \frac{3}{302}
$$

So, the scale factor is 3:302 or $ \frac{3}{302} $

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✔ Final Answer:

The scale factor of the model to the actual Statue of Liberty is 3:302.

This means that every 3 inches on the model represents 302 inches (or 25.17 feet) on the actual statue.

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Optional: Scale Factor as a Decimal

If you want it as a decimal:
$$
\frac{3}{302} ≈ 0.009934
$$
So, the model is about 0.9934% the size of the original.

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Let me know if you'd like to check proportions or set up a cross-multiplication equation as requested in the problem!