SOLUTION: The height of a right circular cone is 24 inches and the radius of the base is 6 inches. A cylindrical hole of diameter 4 inches is drilled through the cone so that the point of th

Algebra ->  Volume -> SOLUTION: The height of a right circular cone is 24 inches and the radius of the base is 6 inches. A cylindrical hole of diameter 4 inches is drilled through the cone so that the point of th      Log On


   

Question 959400: The height of a right circular cone is 24 inches and the radius of the base is 6 inches. A cylindrical hole of diameter 4 inches is drilled through the cone so that the point of the drill follows the altitude of the cone. Determine the volume of the solid region that remains.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
watch for the ratio between the height and the radius. The diameter of the hole is 4 inches so the radius of the hole is 2 inches. The conical portion removed in the hole drilling is a height of 2%2A%2824%2F6%29=8 inches heightl The volume is cross%288%2Api%2A2%5E2=32pi%29%281%2F3%29pi%2A2%5E2%2A8=%2832%2F3%29pi. A purely cylindrical portion below this conical space is of volume %2824-8%29%2Api%2A2%5E2=16%2A4%2Api=64pi. The total space removed in the drilling is %2832%2F3%29pi%2B64pi=%28224%2F3%29pi.

New volume is original volume minus drilled-out volume.
highlight%28NewVolume=cross%2824%2Api%2A6%5E2-96pi%29%29%281%2F3%29pi%2A6%5E2%2A24-%28224%2F3%29pi.
That is so you can understand. Simplify from that.

(should be better now)