Question

guided practice
identify the scale factor.

1. grizzly bear model

height (in.) 84 6

1. moray eel model

length (ft) 5 1\frac{1}{2}

1. in a photograph, a sculpture is 4.2 cm tall and 2.5 cm wide. the scale factor is \frac{1}{16}. find the size of the actual sculpture.
2. ms. jackson is driving from south bend to indianapolis. she measures a distance of 4.3 cm between the cities on her indiana road map. the map scale is 1 cm:48 km. what is the actual distance between these two cities?

Explanation:

Step1: Find the scale factor for Grizzly Bear

Scale factor = $\frac{\text{Model Height}}{\text{Actual Height}}=\frac{6}{84}=\frac{1}{14}$

Step2: Find the scale factor for Moray Eel

First, convert $1\frac{1}{2}=\frac{3}{2}$. Then scale factor = $\frac{\text{Model Length}}{\text{Actual Length}}=\frac{\frac{3}{2}}{5}=\frac{3}{2}\times\frac{1}{5}=\frac{3}{10}$

Step3: Find the actual size of the sculpture

If the scale factor is $\frac{1}{16}$, then actual height = $4.2\div\frac{1}{16}=4.2\times16 = 67.2$ cm, actual width = $2.5\div\frac{1}{16}=2.5\times16=40$ cm

Step4: Find the actual distance between the cities

If the scale is $1$ cm:$48$ km and the map distance is $4.3$ cm. Then actual distance = $4.3\times48=(4 + 0.3)\times48=4\times48+0.3\times48=192+14.4 = 206.4$ km

Answer:

1. The scale factor for the Grizzly Bear is $\frac{1}{14}$.
2. The scale factor for the Moray Eel is $\frac{3}{10}$.
3. The actual height of the sculpture is $67.2$ cm and the actual width is $40$ cm.
4. The actual distance between South Bend and Indianapolis is $206.4$ km.