Question

What is the volume of a rectangular prism when the lengths are tripled?

Answer 1

The volume increases by a factor of `3^3` or `27`

Explanation:

Let's pretend that the volume `V` can be described in algebra as follows:

`V=lxxwxxh`

Where `l` is length, `w` is width, and `h` is height. Let's increase all of those measures by a factor of 3. The new volume will be written as `V'`:

`V'=3lxx3wxx3h`

Using the transitive property, we can rearrange:

`V'=3xx3xx3xxlxxwxxh`

Notice we now have `lxxwxxh` by itself:

`V'=3^3xxlxxwxxh=3^3xxV`

You can now see that if all the linear dimensions of the prism are tripled, we get an increase of 3^3 to the original volume:

`color(green)(V'=27V`

Answer 2

The volume becomes 27 times the initial volume of rectangular prism when lengths are tripled

Explanation:

Let `l, b` & `h` be the length & width of rectangular cross-section & `l` be the length of prism then its volume `V`
`V=lbh`
Now, all ;engths are tripled i.e. dimensions become `3l, 3b, 3h` then the volume `V'` of new rectangular prism
`V'=3l\cdot3b\cdot3h=27lbh=27V`
The volume becomes 27 times the initial value