Saturday, February 16, 2013

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?




Friday, February 15, 2013

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?