Math CentralQuandaries & Queries


Question from Eyuel:

a scoop of ice cream has a 3-inch radius how tall should the ice cream cone at the same radius be in order to contain all of the ice creams inside the cone

Hi Eyuel,

Assume the ice cream scoop is a sphere of radius $r$ inches and then the top of the cone will also have radius $r$ inches. Suppose the height of the cone is $h$ inches. You want the volume of the scoop of ice cream to equal the volume of the cone.

Use the equations for the volume of a sphere and the volume of a cone to write an equation that says these two volumes are equal. Simplify as much as you can. This will give you an equation for $h$ in terms of $r.$ Substitute $r = 3$ inches.


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