Question 1167048
A right circular cylinder of radius r and height h has volume given by V=πr^2h and surface area given by A=2πr^2+2πrh.
 A manufacturer must design a cylindrical can that can hold 800π cubic cm of liquid.
 Express the amount of material needed to make the can as a function of its radius, r.
:
Volume
{{{pi*r^2*h = 800pi}}}
divide both sides by pi
{{{r^2*h = 800}}}
{{{h = 800/r^2}}}
:
Area
{{{A = (2pi*r^2) + (2pi*r*h)}}}
replace h with {{{800/r^2}}}
{{{A = (2pi*r^2) + (2pi*r*(800/r^2))}}}
Cancel r
{{{A = (2pi*r^2) + (2*pi*(800/r))}}}
simplify
{{{A = 2pi*(r^2+(800/r))}}} amt of material as a function of r