Tom has an ice cream cone. The glob of ice cream in the top is a perfect sphere with a circumference of 6π inches. It sits in a cone perfectly at the center. Also the distance from the bottom of the ice cream to the tip of the cone is 1/3 the distance from the bottom of the ice cream to the opening of the cone. What is the volume of the cone not filled with ice cream?
I assume this means that the ice cream is half in and half out of the cone, in which case:
The diameter of the cone is 6 inches (big cone!) as circumference = π*diameter.
Hence bottom of cone is 3 inches below cone opening.
Hence depth of cone = 3 + (1/3)*3 = 4 inches.
Volume of cone, Vc = (1/3)π*32 *4 in3
Volume of ice-cream hemisphere inside cone, Vi = (1/2)*(4/3)*π*33 in3.
So volume of cone not filled with ice cream V = Vc - Vi