Question

the table below gives the dimensions of a sculpture and a scale model of the sculpture. find the scale factor of the model. (the scale factor to get the model from the sculpture.) write your answer as a fraction in simplest form. | | sculpture | model | | --- | --- | --- | | length (inches) | 27 | 6 | | width (inches) | 18 | 4 | | height (inches) | 36 | 8 | scale factor: |

Explanation:

Step1: Recall scale factor formula

The scale factor from the sculpture to the model is the ratio of the model's dimension to the sculpture's dimension. So, for a dimension, scale factor \( = \frac{\text{Model's dimension}}{\text{Sculpture's dimension}} \).

Step2: Calculate using length

Using length: Sculpture length \( = 27 \), Model length \( = 6 \). So scale factor \( = \frac{6}{27} \). Simplify this fraction by dividing numerator and denominator by their greatest common divisor (GCD). The GCD of 6 and 27 is 3. So \( \frac{6\div3}{27\div3} = \frac{2}{9} \). Let's check with width: Sculpture width \( = 18 \), Model width \( = 4 \). \( \frac{4}{18} = \frac{2}{9} \) (dividing numerator and denominator by 2). Check with height: Sculpture height \( = 36 \), Model height \( = 8 \). \( \frac{8}{36} = \frac{2}{9} \) (dividing numerator and denominator by 4). So the scale factor is consistent.

Answer:

\(\frac{2}{9}\)