Question 209457
a 39 ounce can of hills bros. coffee requires 188.5 square inches of aluminum.
 if its height is 7 inches, what is its radius?
:
The cylinder surface area formula: S.A. = {{{2*pi*r^2}}} + {{{2*pi*r*h}}}
S.A. = 188.5; h = 7
{{{2*pi*r^2}}} + {{{2*pi*r*7}}} = 188.5
{{{2*pi*r^2}}} + {{{14*pi*r}}} = 188.5
Divide by {{{2*pi}}}
r^2 + 7r = {{{188.5/(2*pi)}}}
r^2 + 7r = 30
:
A quadratic equation
r^2 + 7r - 30 = 0
:
Factor this to
(r+10)(r-3) = 0
;
Positive solution
r = 3 inches is the radius
:
:
Check solution
{{{2*pi*3^2}}} + {{{2*pi*3*7}}} = 
56.55 + 131.95 = 188.5