Question 324256
The volume of a cylinder is,
{{{V=pi*r^2*H}}}
{{{h=r+8}}}
{{{V=pi*r^2(r+8)}}}
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When V=1000 cc,
{{{V=pi*r^2(r+8)=1000}}}
{{{r^3+8r^2=1000/pi}}}
{{{r^3+8r^2-1000/pi=0}}}
I used the cubic equation solver at www.1728.com/cubic.htm to get the roots of the cubic equation (two roots are complex, the remaining root is real). 
{{{r= 4.96}}}cm
{{{h=r+8=12.96}}}cm
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When V=1500 cc,
{{{r^3+8r^2-1500/pi=0}}}
{{{r= 5.87}}}cm
{{{h= 13.87}}}cm
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({{{4.96 <= r <= 5.87}}})
({{{12.96 <= h <= 13.87}}})
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