<PRE><B>Question 1016717</B>
A water tank, open at top, is hemispherical at the bottom and cylindrical above it.
The radius is 12 meters and the capacity is 3312 pie meter cube.
Find the ratio of the surface areas of the spherical and cylindrical portions.
{{{(2*pi*r^2)/(2*pi*r*h)}}} = {{{r/h}}}; canceled {{{2*pi*r}}}
:
r = 12; Find h of the cylinder portion
V = Hemisphere vol + cylinder vol:
{{{2/3}}}{{{pi*12^3}}} + {{{pi*12^2*h}}} = {{{3312*pi}}}
divide thru by pi; do the math
{{{2/3}}}*1728 + 144h = 3312
1152 + 144h = 3312
144h = 3312 - 1152
144h = 2160
h = 2160/144
h = 15 meters high
:
The surface area ratio: {{{r/h}}} = {{{12/15}}} = {{{4/5}}}
</PRE>