Question

An architect is designing a scale model that is similar to an actual building in the shape of a triangular prism. If the ratio of the height of her scale model to the height of the actual building is 1:98, what is the ratio of the volume of the scale model to the volume of the building?

Answer 1

The ratio of the volume of the scale model to the volume of the building is
`(1)/(941,192)`

Explanation:

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube, and the ratio of its corresponding sides is equal to the scale factor

so

Let

z-----> the scale factor

x----> the volume of the scale

y----> the volume of the building

`z^(3)=(x)/(y)`

In this problem we have

`z=(1)/(98)`

substitute

`((1)/(98))^(3)=(x)/(y)`

`((1)/(941,192))=(x)/(y)`

rewrite

`(x)/(y)=(1)/(941,192)`