Question

An ice cream cone is made of a cone shape and half a sphere shape. Explain how you could find the volume of the entire ice cream cone.

Answer 1

Call the radius r and the height of the cone h.  The formula for the volume of a cone is r^2*h*pi/3, and the formula for the volume of a sphere is 4r^3/3, so half of a sphere has volume 2r^3/3.  Adding these, our answer is:

$\frac{r^2 h \pi+r^3}{3}$