Question 482350
A pond contains 7.2 cubic yards of water. what is the volume of the water in cubic meters to the nearest tenth?
<pre>
We make and use unit fractions from 1yd=3ft, 1ft=12in, 1in=2.54cm, 1m=100cm


{{{7.2yd^3 = (expr((7.2yd*yd*yd)/1)*expr( (3ft*3ft*3ft)/(1yd*1yd*1yd) )*

expr( (12in*12in*12in)/(1ft*1ft*1ft) )*

expr( (2.54cm*2.54cm*2.54in)/(1in*1in*1in) )*

expr( (1m*1m*1m)/(100cm*100cm*100cm)) ) 

 }}}

Cancelling the yd:

{{{7.2yd^3 = (expr((7.2cross(yd)*cross(yd)*cross(yd))/1)*expr( (3ft*3ft*3ft)/(1cross(yd)*1cross(yd)*1cross(yd)) )*

expr( (12in*12in*12in)/(1ft*1ft*1ft) )*

expr( (2.54cm*2.54cm*2.54in)/(1in*1in*1in) )*

expr( (1m*1m*1m)/(100cm*100cm*100cm)) ) 

 }}}

Cancelling the ft:

{{{7.2yd^3 = (expr((7.2cross(yd)*cross(yd)*cross(yd))/1)*expr( (3cross(ft)*3cross(ft)*3cross(ft))/(1cross(yd)*1cross(yd)*1cross(yd)) )*

expr( (12in*12in*12in)/(1cross(ft)*1cross(ft)*1cross(ft)) )*

expr( (2.54cm*2.54cm*2.54in)/(1in*1in*1in) )*

expr( (1m*1m*1m)/(100cm*100cm*100cm)) ) 

 }}}

Cancelling the in:

{{{7.2yd^3 = (expr((7.2cross(yd)*cross(yd)*cross(yd))/1)*expr( (3cross(ft)*3cross(ft)*3cross(ft))/(1cross(yd)*1cross(yd)*1cross(yd)) )*

expr( (12cross(in)*12cross(in)*12cross(in))/(1cross(ft)*1cross(ft)*1cross(ft)) )*

expr( (2.54cm*2.54cm*2.54in)/(1cross(in)*1cross(in)*1cross(in)) )*

expr( (1m*1m*1m)/(100cm*100cm*100cm)) ) 

 }}}

Cancelling the cm:

{{{7.2yd^3 = (expr((7.2cross(yd)*cross(yd)*cross(yd))/1)*expr( (3cross(ft)*3cross(ft)*3cross(ft))/(1cross(yd)*1cross(yd)*1cross(yd)) )*

expr( (12cross(in)*12cross(in)*12cross(in))/(1cross(ft)*1cross(ft)*1cross(ft)) )*

expr( (2.54cross(cm)*2.54cross(cm)*2.54cross(cm))/(1cross(in)*1cross(in)*1cross(in)) )*

expr( (1m*1m*1m)/(100cross(cm)*100cross(cm)*100cross(cm))) ) 

 }}}

Ignoring the 1s we have:

{{{7.2yd^3=expr((7.2*3*3*3*12*12*12*2.54*2.54*2.54*m*m*m)/(100*100*100)) =5.504794977m^3}}}

Edwin</pre>