Question 947652
Apparently that tin maker can flatten the cubical can into and odd shaped sheet of tin with the same surface area,
and then manage to cut from that sheet the necessary pieces to make the 10 cylindrical cans, wasting only 12% of the material.
The total surface area of a cube with a {{{50cm}}} side is 
{{{6(50cm)^2=6*(2500cm^2)=15000cm^2}}} .
Wasting {{{"12%"}}} means using {{{"100%"-"12%"="88%"=88/100=0.88}}} .
{{{"88%"}}} of {{{15000cm^2}}} is
{{{0.88*15000cm^2=13200cm^2}}} .
The total surface area of a cylinder with a {{{7cm}}} radius and a height of {{{h}}}{{{cm}}} is
{{{2*pi*(7cm)^2+2*pi*(7cm)*h}}}{{{cm=2*pi*7*(7+h)}}}{{{cm^2=14pi*(7+h)}}}{{{cm^2}}} .
The total surface area of {{{10}}} such cylinders is
{{{140pi(7+h)}}}{{{cm^2}}} .
Since that is supposed to be the {{{13200cm^2}}} used, our equation is
{{{140pi(7+h)=13200}}}
Solving for {{{h}}} :
{{{140pi(7+h)=13200}}}
{{{7+h=13200/140pi}}}
{{{h=13200/140pi-7}}}
The approximate solution is {{{highlight(h=23.012)}}}{{{cm}}} .