Question 1189137
An open-topped cylindrical cup is to have volume 125 cm3.
{{{pi*r^2*h}}} = 125
h = {{{125/(pi*r^2)}}}
:
 Determine the minimum possible amount of material used in making this pot?
A = the area of the material required
A = {{{(pi*r^2)+(2pi*r*h)}}}
A = {{{pi*r(r+2h)}}}
replace h with {{{125/(pi*r^2)}}}
A = {{{pi*r(r+2(125/(pi*r^2)))}}}
A = {{{pi*r(r+(250/(pi*r^2)))}}}
A = {{{(pi*r^2) + (250/r)}}}
Graphically, radius on the x axis, area on y axis
{{{ graph( 300, 200, -4, 8, -100, 200, (pi*x^2)+(250/x)) }}}
minimum area when radius = 3.5 cm
Find the height
h = {{{125/(pi*3.5^2)}}}
h = 3.25 cm is the height for minimum area
:
:
Check, find the volume using these dimensions
V = {{{pi*3.5^2*3.25}}}
V = 125.07 ~ 12