Acone is placed inside a cylinder. the cone has half the radius of the cylinder, but the height of each figure is the same. the cone is tilted at an angle so its peak touches the edge of the cylinder’s base. what is the volume of the space remaining in the cylinder after the cone is placed inside it?

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