Question 935226
I expect that what is mean is that the cone looks like this:
{{{drawing(300,300,-8,8,-8,8,
circle(0,0,0.1),green(triangle(-7,0,7,0,0,-7)),
red(arc(0,0,14,14,180,360)),
arrow(0,0.1,0,7),arrow(0,7,0,0.1),
arrow(0,-0.1,0,-6.9),arrow(0,-6.9,0,-0.1),
locate(0.1,4,7cm),locate(0.1,-3,7cm)
)}}} That means the radius of the hemisphere, the radius of the cone, and the height of the cone are all 7 cm.
The volume of a sphere of radius {{{r}}} is {{{(4/3)*pi*r^3}}} , and the volume of half a sphere is {{{1/2}}} of that.
So the volume of the hemispherical (half a sphere) top part, in cubic centimeters, is
{{{(1/2)*(4/3)*pi*7^3=(2/3)*pi*7^3}}} .
A cone of radius {{{r}}} and height {{{h}}} has a volue of {{{(1/3)*pi*r^2*h}}} ,
so the volume of the conical bottom part, in cubic centimeters, is
{{{(1/3)*pi*7^2*7=(1/3)*pi*7^3}}} .
The volume, in cubic centimeters, of the whole thing is the sum of the volumes of top and bottom parts:
{{{(2/3)*pi*7^3+(1/3)*pi*7^3=pi*7^3=343pi=about1078}}} (rounding, and using 3.1416 for {{{pi}}} ).