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?

Guest Feb 28, 2020

#1**+4 **

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*3^{2} *4 in^{3}

Volume of ice-cream hemisphere inside cone, Vi = (1/2)*(4/3)*π*3^{3} in^{3}.

So volume of cone not filled with ice cream V = Vc - Vi

Alan Feb 29, 2020