Question 1025412
r for radius, h for height, 
{{{h=r+5}}}


{{{h*pi*r^2=32}}}



{{{(r+5)pi*r^2=32}}}
{{{r^2(r+5)pi=32}}}
{{{r^3+5r^2=32/pi}}}
{{{r^3+5r^2-32/pi=0}}}


Use any method you know for finding roots of that equation.  This is not something that Rational Roots Theorem will help with.  Maybe try a graphing tool.




{{{graph(400,400,-3,7,-3,7,x^3+5x^2-32/pi)}}}


{{{graph(400,400,-3,12,-3,12,x^3+5x^2-32/pi)}}}


Closer look:
{{{graph(400,400,0,3,0,2,x^3+5x^2-32/pi)}}}