the volume of a sphere with radius r is

V = (4/3)*r^3*pi

the volume of a cone with the same base radius as the sphere and height h

V = (1/3)*r^2*pi*h

since they have the same volume we can write

(4/3)*r^3*pi = (1/3)*r^2*pi*h multiply both sides by 3/pi

4*r^3 = r^2*h multiply both sides by 1/(r^3)

4 = h/r

h/r = 4

h : r = 4 : 1