Question 875308
{{{S(r)=2(pi)r^2+800/r}}}
 
(a) Using {{{pi=3.14}}} and rounding to 2 decimal places,
{{{S(2)=2(pi)2^2+800/2=2*3.14*4+400=25.15+400=425.12}}}
{{{S(3)=2(pi)3^2+800/3=2*3.14*9+266.67=56.52+266.67=323.19}}}
{{{S(4)=2(pi)4^2+800/4=2*3.14*16+200=100.48+200=300.48}}}
{{{S(6)=2(pi)6^2+800/6=2*3.14*36+133.33=226.08+133.33=359.41}}}
 
(b) The smallest {{{S(r) we found was {{{S(4)=300.48}}}
so the radius that minimizes the surface area is approximately {{{highlight(4cm)}}} .
 
(c) The less surface area of metal used, the cheapest the can,
so minimizing the surface area reduces costs for the company.
That could lead to more profits.