Question 365679
a cylindrical aluminum can has a volume of 500 cubic centimeters.
 if each square centimeter of aluminum cost .05 cents, express the cost
 of material for the can as a function of the radius r of the can.
:
Use the volume equation to get h in terms of r
{{{pi*r^2*h}}} = 500
Divide both sides by {{{pi*r^2}}}
h = {{{500/((pi*r^2))}}}
:
The surface area of a cylinder including the two ends
S.A. = {{{2*pi*r*h}}} + {{{2*pi*r^2}}}
Get the surface area in terms of r, replace h with {{{500/((pi*r^2))}}}
S.A. = {{{2*pi*r*(500/(pi*r^2))}}} + {{{2*pi*r^2}}}
we can cancel pi*r
S.A. = {{{2*(500/r)}}} + {{{2*pi*r^2}}}
Factor out 2
S.A. = 2({{{(500/r) + (pi*r^2)}}})
To find the cost, multiply by .05
C(r) = .05*2({{{(500/r) + (pi*r^2)}}})
:
C(r) = .1({{{(500/r) + (pi*r^2)}}}); cost of material in terms of r