Question
all your work. 24. The Statue of Liberty is about 152 feet tall. An artist creates a model of the Statue of Liberty using a scale factor of \( \frac{1}{32} \). How tall is the artist's model? ill
Ask by Fitzgerald Riley. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The artist's model of the Statue of Liberty is 4.75 feet tall.
Solution
To find the height of the artist's model of the Statue of Liberty, we can use the scale factor provided. The known conditions are:
- Height of the Statue of Liberty: \( H = 152 \) feet
- Scale factor: \( S = \frac{1}{32} \)
We can calculate the height of the model \( h \) using the formula:
\[
h = H \times S
\]
Now, let's perform the calculation step by step:
1. Substitute the known values into the formula:
\[
h = 152 \times \frac{1}{32}
\]
2. Calculate the multiplication:
\[
h = \frac{152}{32}
\]
Now, let's simplify \( \frac{152}{32} \).
I'll perform the calculation to find the height of the artist's model.
Calculate the value by following steps:
- step0: Calculate:
\(\frac{152}{32}\)
- step1: Reduce the fraction:
\(\frac{19}{4}\)
The height of the artist's model of the Statue of Liberty is:
\[
h = \frac{152}{32} = 4.75 \text{ feet}
\]
Thus, the artist's model is approximately 4.75 feet tall.
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Simplify this solution The Deep Dive
The height of the artist's model can be calculated by multiplying the actual height of the Statue of Liberty by the scale factor. So, \( 152 \, \text{feet} \times \frac{1}{32} = 4.75 \, \text{feet} \). That means the artist's model would stand about 4 feet and 9 inches tall! This little replica offers a fun way to explore concepts of scaling and proportions. Not only does it bring the iconic statue down to a manageable size, but creating models like this also sparks a love for architecture and design, as artists and designers constantly work within scaled dimensions in their projects!
