Question

If the ratio of the sides of two similar prisms is 4:1. Is the ratio of the volume of the prisms the same? (4:1)

Answer 1

The ratio of their volumes is not the same 4:1, but
`(4:1)^3` = 64:1.

Explanation:

Measurements in Similar Figures

In similar figures, if the ratio of any of these corresponding lengths is expressed as a:b then the ratio of the other corresponding lengths can also be expressed as a:b.

In similar figures, if the ratio of any of these corresponding lengths is expressed as a:b then the ratio of the areas can be expressed as (a:b)^2 and the ratio of the volumes can be expressed as (a:b)^3.

We are given the ratio of the sides of two similar prisms as 4:1. The ratio of their volumes is not the same 4:1, but
`\mathbf{(4:1)^3}` = 64:1.