Question 587936
An ice cream cone is packed full of ice cream and a generous hemisphere (half of sphere) of ice cream is placed on top.
 If the volume of ice cream inside the cone is the same as the volume of ice cream outside the cone,
 find the height of the cone (minus the hemisphere) given that the diameter of the hemisphere is 8cm.
:
Formula for a the volume of a cone: V = {{{1/3}}}{{{pi*r^2*h}}}
For the volume of a hemisphere: V = {{{1/2}}}*{{{4/3}}}{{{pi*r^3}}}
:
With a diameter of 8, the radius = 4 cm
:
{{{1/3}}}{{{pi*4^2*h}}} = {{{1/2}}}*{{{4/3}}}{{{pi*4^3}}}
:
{{{1/3}}}{{{pi*16*h}}} = {{{4/6}}}{{{pi*64}}}
{{{1/3}}}{{{pi*16*h}}} = {{{2/3}}}{{{pi*64}}}
multiply both sides by 3
{{{pi*16*h}}} = {{{2*pi*64}}}
{{{pi*16*h}}} = {{{pi*128}}}
divide both sides by {{{pi}}}
16h = 128
h = 128/16
h = 8 cm is the height of the cone