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

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Jun 19, 2018

Answer:

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

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Ben Share
Jun 19, 2018

Answer:

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#

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