Math Problem Statement

The table below gives the dimensions of a statue and a scale drawing of the statue. Find the scale factor of the drawing. (The scale factor to get the drawing from the statue.) Write your answer as a fraction in simplest form.

Solution

To find the scale factor of the drawing relative to the statue, we divide the dimensions of the drawing by the corresponding dimensions of the statue. Let's compute:

  1. Height: Scale factor for height=636=16\text{Scale factor for height} = \frac{6}{36} = \frac{1}{6}

  2. Length: Scale factor for length=530=16\text{Scale factor for length} = \frac{5}{30} = \frac{1}{6}

Since both height and length have the same ratio, the scale factor is: 16\frac{1}{6}

Thus, the correct answer is: 16\boxed{\frac{1}{6}}

Do you have any questions or need further clarification?


Here are 5 related questions for deeper understanding:

  1. What does it mean if two objects have a scale factor of 1?
  2. How do you convert a scale factor from a fraction to a percentage?
  3. How would the dimensions change if the scale factor were 12\frac{1}{2}?
  4. Can a scale factor be greater than 1? What would that represent?
  5. How can we check if a scale drawing maintains the same proportions as the original?

Tip: Always reduce fractions to their simplest form when calculating scale factors to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Ratios
Proportions
Scale Factor

Formulas

Scale factor = Drawing dimension / Statue dimension

Theorems

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Suitable Grade Level

Grades 5-7