Question

The height of a circular tower is 179 meters and its diameter is 48 meters. (Assume that the building is a perfect cylinder). What is the volume of a 1: 166 scale model in cm^3?

Answer 1

The definition of a scale of 1: 166 will mean that the scale of 1 in the model will be equivalent to 166 times the measurement in the real model, therefore we will have that the height would be 166 times smaller than the 179m given:

`h = (179m)/(166) = 1.078m = 107.8cm`

The same for the diameter,

`\phi = (48m)/(166)= 0.2891m = 28.91cm`

The volume of a cylinder is given as

`V = (\pi r^2)(h)`

`V = (\pi ((d)/(2))^2)(h)`

`V = (\pi (( 28.91)/(2))^2)(107.8)`

`V = 70762.8cm^3`

Therefore the volume would be
`V = 70762.8cm^3`