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

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1
Jun 19, 2018

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 $V$
$V = l b h$
Now, all ;engths are tripled i.e. dimensions become $3 l , 3 b , 3 h$ then the volume $V '$ of new rectangular prism
$V ' = 3 l \setminus \cdot 3 b \setminus \cdot 3 h = 27 l b h = 27 V$
The volume becomes 27 times the initial value

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Ben Share
Jun 19, 2018

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:

$V = l \times w \times h$

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 $V '$:

$V ' = 3 l \times 3 w \times 3 h$

Using the transitive property, we can rearrange:

$V ' = 3 \times 3 \times 3 \times l \times w \times h$

Notice we now have $l \times w \times h$ by itself:

$V ' = {3}^{3} \times l \times w \times h = {3}^{3} \times V$

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

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