Final answer:
To find the missing actual depth of the water tower with a scale factor of 1:12, set up the proportion 1/12 = 32/X, solve for X, and then convert centimeters to meters to get the actual depth of 3.84 meters.
Step-by-step explanation:
To find the missing actual depth of the water tower using a scale factor, we can set up a proportion based on the given information. The scale factor tells us how the dimensions of the model relate to the actual dimensions. In this case, the scale factor is 1:12, meaning 1 unit on the model represents 12 units in actual size.
First, write the proportion: Since the depth of the model water tower is 32 cm, we can express the proportion as 1 (model unit) / 12 (actual units) = 32 cm (model depth) / X cm (actual depth).
Next, we solve for X by cross-multiplying:
- 1 * X = 12 * 32
- X = 12 * 32
- X = 384 cm
Since the question asks for the actual depth in meters, we must convert centimeters to meters:
- 384 cm = 384 / 100 m
- X = 3.84 m
Therefore, the actual depth of the water tower is 3.84 meters.