Question

An architect built a scale model of a shopping mall. On the model, a circular fountain is 21 inches tall and 17.5 inches in diameter. If the actual fountain is to be 6 feet tall, what will its diameter be?

Answer 1

The diameter is 5ft

Explanation:

Given

`Height : Diameter = 21\ in: 17.5\ in`

Required

Determine the diameter when the height is 6ft

Recall that the scale is a ratio of height to diameter;

So 6ft height can be represented on the following scale model;

`Height : Diameter = 6ft : x`

Convert to fraction

`(Height)/(Diameter) = (6)/(x)` ---- (1)

Recall that:

`Height : Diameter = 21\ in: 17.5\ in`

Convert to fraction

`(Height)/(Diameter) = (21 )/(17.5)` ---- (2)

Equate (1) & (2)

`(6)/(x)= (21 )/(17.5)`

Cross Multiply

`21 * x = 6 * 17.5`

`21x = 105`

`x = 105/21`

`x = 5`

Hence, the diameter is 5ft