Math CentralQuandaries & Queries


Question from Darah, a student:

A manufacturer is making a large, hollow, ice cream cone to serve as an ad for a local Baskin-Robbins. The ice cream cone is made up of a cone with height 8 feet, topped by a hemisphere with radius 6 feet. How much ice cream could the hollow object hold? If a gallon is 0.13368 cubic feet, how many gallons does it hold? If 3 gallons of Baskin-Robbins heavy cream chocolate blend weighs 24 pounds, how much would the ice cream cone weigh, excluding the weight of the construction material?

Hi Darah.

Step 1:

You need to first, find the volume of the object. It is made up of two pieces: a hemisphere and a cone. So if you find the volume of the hemisphere (you can use the formula V = (2/3) π r3 for this) and add that to the volume of the cone (use the cone volume formula V = (1/3) π r2 h for this), then you have the volume of the overall object.

Step 2:

This volume you got was in cubic feet (because all the measurements were in feet). To convert to gallons, divide by the conversion factor you were given.

Step 3:

Now that you know the number of gallons, you can multiply that by 24 / 3 (24 pounds per 3 gallons) to get the pounds of ice cream.

Now you're done. Give yourself a treat (maybe some ice cream...?)

Stephen La Rocque

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