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.

length (inches)	sculpture	model
width (inches)	42	7
height (inches)	30	5
	54	9

scale factor:

Explanation:

Step1: Recall scale - factor formula

The scale factor from the sculpture to the model is given by the ratio of the dimension of the model to the dimension of the sculpture. We can use any of the three dimensions (length, width, or height). Let's use the length.

Step2: Calculate the scale - factor

The length of the sculpture is 42 inches and the length of the model is 7 inches. The scale factor $k$ is $k=\frac{\text{Model length}}{\text{Sculpture length}}=\frac{7}{42}$.

Step3: Simplify the fraction

We simplify $\frac{7}{42}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 7. So, $\frac{7\div7}{42\div7}=\frac{1}{6}$.

Answer:

$\frac{1}{6}$