Question 894206
When I try to put a ball halfway into a cone, I need to deform the bottom half a bit:{{{drawing(200,350,-4,4,-9,5,
triangle(-3,0,3,0,0,-8),
red(circle(0,0,3))
)}}}
However, once I get the bottom half into the cone, from the outside it looks like this:
{{{drawing(200,350,-4,4,-9,5,
triangle(-3,0,3,0,0,-8),
red(arc(0,0,6,6,180,360))
)}}} , I can calculate the total volume as the volume of the come plus half the volume of a sphere.
The circular base of the cone, and the sphere have a diameter of {{{6}}} units,
so the radius is {{{3}}} units.
The volume of a sphere of radius {{{R}}} is {{{4pi*R^3/3}}} .
The volume of a half of sphere of radius {{{R}}} is {{{2pi*R^3/3}}} .
If the radius is {{{R=3}}} , that volume is
{{{2pi*3^3/3=2*pi*27/3=18pi}}}
The volume of a cone of height {{{h}}} and base radius {{{R}}} is {{{pi*R^2*h/3}}}.
If the radius is {{{R=3}}} , and the height is {{{h=8}}} , that volume is
{{{pi*3^2*8/3=pi*9*8/3=24pi}}} .
Adding half a sphere plus a cone, the total volume is
{{{18pi+24pi=42pi}}}