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| Math Central | Quandaries & Queries |
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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.
Penny
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