The volume of the cylinder is:
Vcy = π r2 h
And using the given conditions that the cone has half the radius of and same height with the cylinder, we have:
Vco = (1/3) π (r/2)2 h
Vco = π r2 h / 12
The volume of the space remaining is the difference between the two volumes. So,
Vs = Vcy - Vco
Vs = π r2 h - π r2 h / 12
Vs = 11 π r2 h / 12
The volume of the space is 11 π r2 h / 12
