Question 80753
A solid metal cylinder of radius 6 cm and height 18 cm is melted down and recast as a cone of radius 6 cm. What is the height of the cone?
:
Vol of cyl = {{{pi*r^2*h}}}
Vol of cone = {{{(pi*r^2*h)/3}}}
:
An easy way to do this:
          Cone Vol = Cylinder Vol
{{{(pi*6^2*h)/3}}} = {{{pi*6^2*18}}}
:
Divide both sides by {{{pi*6^2}}}; you have
{{{h/3}}} = 18
:
h = 18 * 3
h = 54 is height of the cone