Question 737621
 the surface area of a cylinder is 1000 pi square centimeters.
 the radius of the cylinder is four times the height.
 what is the height of the cylinder.
:
LET x = the height
"radius is 4 time the height" therefore
4x = the radius
:
S.A. = {{{2*pi*r^2}}} + {{{2*pi*r*h}}}
so we have
{{{2*pi*(4x)^2}}} + {{{2*pi*(4x)*x}}} = {{{1000pi}}}
divide equation by 2pi
{{{(4x)^2 + 4x*x}}} = 500
{{{16x^2 + 4x^2}}} = 500
{{{20x^2}}} = 500
divide both sides by 20
{{{x^2}}} = 25
x = {{{sqrt(25)}}}
x = 5 is the height
:
You can check the math on this,