Final answer:
To find the volume of the remaining object post the removal of a hemisphere, subtract the hemisphere's volume from the cylinder's volume, resulting in 1408π/3 cubic units.
Step-by-step explanation:
The student is asking how to calculate the volume of a remaining object after a hemisphere with a radius equal to the base of the cylinder is removed from the tip of a cylinder of height 10 units and radius 8 units. To find the volume of the remaining object, we need to first calculate the volume of the original cylinder using the formula V_cylinder = πr²h, which gives us 640π cubic units. Next, we calculate the volume of the hemisphere using the formula V_hemisphere = (2/3)πr³, which gives us 256π/3 cubic units. The volume of the remaining object is then the volume of the cylinder minus the volume of the hemisphere, resulting in 640π - 256π/3 = 1408π/3 cubic units.