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:

$h = \frac{179m}{166} = 1.078m = 107.8cm$

The same for the diameter,

$\phi = \frac{48m}{166}= 0.2891m = 28.91cm$

The volume of a cylinder is given as

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

$V = (\pi (\frac{d}{2})^2)(h)$

$V = (\pi (\frac{ 28.91}{2})^2)(107.8)$

$V = 70762.8cm^3$

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