A scale model of a suspension bridge tower is geometrically similar to the actual structure. The ratio of the corresponding dimensions of the model to the actual tower is 1 : 400. If the actual tower stands at a height of 72 m, what is the height of the model?

The correct option is 18 cm.

Step 1: Understand the scale ratio
A scale model is geometrically similar to the actual structure. The ratio of the corresponding dimensions of the model to the actual tower is given as 1 : 400.

This ratio relationship can be written as:

$\frac{\text{Height of Model}}{\text{Height of Actual Tower}}=\frac{1}{400}$

Step 2: Calculate the height of the model in meters
We are given that the actual tower stands at a height of 72 m. Substituting this value into the equation gives:

$\text{Height of Model}=\frac{72\text{m}}{400}$

$\text{Height of Model}=0.18\text{m}$

Step 3: Convert meters to centimeters
Since 1 meter is equal to 100 centimeters (1 m = 100 cm), we convert the height to centimeters by multiplying by 100:

$\text{Height of Model}=0.18\times 100\text{cm}=18\text{cm}$

Thus, the height of the model is 18 cm.