Question 550972
Height of cone is 8cm and curved surface area is 188.4cm sq. 
Then find the volume of cone.
:
The curved portion surface area of a cone: {{{A = pi*r*sqrt(r^2+h^2)}}}
:
Find r
{{{pi*r*sqrt(r^2+8^2)}}} = 188.4
{{{r*sqrt(r^2+64)}}} = {{{188.4/pi}}}
{{{r*sqrt(r^2+64)}}} = 59.9696
Square both sides
{{{r^2(r^2+64)}}} = 3596.35
{{{r^4+64r^2 - 3596.35}}} = 0
solve this with the quadratic formula
the positive solution
r^2 ~ 36, which is what we want to find the volume

:
Find the volume; {{{V = 1/3}}}*{{{pi*r^2*h}}}
{{{V = 1/3}}}*{{{pi*36*8}}}
V = 301.6 cu cm