Question 152460
A shipping box measures 14 1/2 inches long by 9 1/8 inches wide by 8 11/16 inches high. What is the volume of the box in cubic feet? Round to the nearest hundredth of a cubic foot.
<pre><font size = 4 color="indigo"><b>
Change {{{14}}}{{{1/2}}}{{{in}}} to the decimal {{{14.5in}}}
Change {{{9}}}{{{1/8}}}{{{in}}} to the decimal {{{9.125in}}}
Change {{{8}}}{{{11/16}}}{{{in}}} to the decimal {{{8.6875in}}}

{{{V=LWH}}}

{{{V=(14.5in)(9.125in)(8.6875in)}}}

{{{V=(14.5)(9.125)(8.6875)(in^3)}}}

{{{V=1149.464844(in)^3}}}

Now put this over {{{1}}}

{{{V=1149.464844(in)^3/1}}}

Now we make a unit fraction, using
inches and feet that is a fraction 
that equals 1, that has equal
numerator and denominator, and which
will cancel away the inches. We know
that {{{12in=1ft}}}. Therefore such a
unit fraction is {{{(1(ft))/(12(in))}}} 

But we need to cancel away {{{(in)^3}}},
so we cube the unit fraction and get
{{{(1^3(ft)^3)/(12^3(in)^3)}}} or
{{{(1(ft)^3)/(1728(in)^3)}}}

Now we multiply by that unit fraction:

{{{V=(1149.464844(in)^3/1)((1(ft)^3)/(1728(in)^3))}}}

Now we can cancel the {{{(in)^3}}}

{{{V=(1149.464844cross((in)^3)/1)((1(ft)^3)/(1728cross((in)^3)))}}}

and all we have left is

{{{V=(1149.464844(ft)^3)/(1728)}}}

Divide that out and get:

{{{V=0.6651995624ft^3}}}

or to the nearest hundredth of a {{{ft^3}}}

{{{V=0.67ft^3}}}

Edwin</pre>