Questions: Rairos, Proportions, and Measurement Finding a scale factor: Same units 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) 63 7 Width (inches) 54 6 Height (inches) 81 9 Scale factor:

Solution Steps

We are given the dimensions of a sculpture and its scale model. Our task is to find the scale factor that transforms the dimensions of the sculpture into those of the model. The scale factor is the ratio of a dimension of the model to the corresponding dimension of the sculpture.

To find the scale factor, we calculate the ratio of each dimension of the model to the corresponding dimension of the sculpture.

1. Length: \[ \text{Scale factor for length} = \frac{\text{Length of model}}{\text{Length of sculpture}} = \frac{7}{63} \]

2. Width: \[ \text{Scale factor for width} = \frac{\text{Width of model}}{\text{Width of sculpture}} = \frac{6}{54} \]

3. Height: \[ \text{Scale factor for height} = \frac{\text{Height of model}}{\text{Height of sculpture}} = \frac{9}{81} \]

We simplify each of the ratios calculated in Step 2 to find the scale factor in its simplest form.

1. Length: \[ \frac{7}{63} = \frac{1}{9} \]

2. Width: \[ \frac{6}{54} = \frac{1}{9} \]

3. Height: \[ \frac{9}{81} = \frac{1}{9} \]

Since the scale factor is consistent across all dimensions (length, width, and height), the scale factor for the model is the same for each dimension.

Final Answer