Question 1001753
A company needs to make a cylindrical can that can hold precisely 0.7 liters of liquid.
 If the entire can is to be made out of the same material, find the dimensions of the can that will minimize the cost.
:
 .7 liters = .7*1000 700 cubic/cm

let r = the radius of the can that has a volume of 700 cm/cm
:
{{{pi*r^2*h}}} = 700
h = {{{700/((pi*r^2))}}}
h = {{{222.817/r^2}}}
The surface area
S.A. = {{{2(pi*r^2)}}} + {{{2*pi*r*h}}}
Factor out 2*pi*r
S.A. = {{{2pi*r(r + h)}}}
replace h with 222.817/r^2
S.A. = {{{2pi*r(r + (222.817/r^2))}}}
:
Graph this equation, radius on the x axis, Surface area on the y axis
{{{ graph( 300, 200, -4, 10, -200, 1000, x-2, 6.28x^2+(1400/x)) }}}
:
Radius for minimum surface area about 4.8 cm
Find the height
h = 222.817/4.8^2
h = 9.67 cm
:
Check: find the vol with these values
V = {{{pi*4.8^2*9.67}}}
V = 700 cu/cm