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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?

 Feb 28, 2020
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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

 Feb 29, 2020
edited by Alan  Feb 29, 2020

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