Ice Cream Cone Math

Have you ever wondered how much ice cream will fit into a cone?   The inside of a cone is also called its volume.  Use the formula below to find the volume of a cone.

• Sam has an ice cream cone that is 5 inches in height, and has a radius of 1.25 inches.  Find the volume of Sam's ice cream cone.  Remember to use cubic inches for labeling the answer :)

• Did you notice that the cone is one-third the volume of a cylinder of equal height?   If the volume of the cone were 8.1 cubic inches, compare the volume of a cylinder with the same radius and height?     

• Compare the volume of different ice cream cones:  Waffle cones, large sugar cones, and small sugar cones.  How much more ice cream do the bigger cones hold?  Is it worth it to buy a bigger cone?

Surface Area of Cylinders

Group Results of Cylinder having Surface Area of 900 cm² 

Radius	Height cm	Volume  cm³	Surface Area cm²	Ratio Surface Area/Volume cm²/cm³
2	70	879.2	904.32	1.03
3	45	1271.7	904.32	0.71
5	24	1884	910.6	0.48
9	7	1780.38	904.32	0.51
10	4	1256	879.2	0.70

1. What things stand out about the data displays?
2. Compare the relationship between radii and heights.  
3. Predict the size other radius/height pairs that fit the pattern. 
4. What are some further questions for this investigation?