Chapter 1: Polynomial Functions
Investigation 1.1—Homemade Waffle Cones
Did You Know?
Italo Marchiony sold homemade ice cream from a pushcart on Wall Street. Often,
his customers wandered off with the ice cream dishes, or worse yet, broke them.
To curb these expenses, Italo baked edible waffle cups with sloping sides and flat
bottoms. He patented his idea in 1903.
Reference: http://www.makeicecream.com/hisoficecrea.html
The local scholarship committee is planning to sell ice cream cones at high school
events. The scholarship committee is interested in serving the ice cream in waffle
cones, and, the committee has a waffle maker that will make circular waffles 21
centimeters in diameter.
Let’s investigate how the scholarship committee can design a waffle cone with the
greatest volume using a circular waffle, with a diameter of 21 centimeters. To do so,
cut out a circle (from paper, not waffle yet) that is 21 centimeters in diameter.
Remove a sector from the circle, and construct a cone. Be sure to tape or glue your
cone together, as we will be investigating the dimensions of the cone that will
maximize its volume.
a. What is the slant height of the cone? Did you need to use a ruler to
determine this measurement? Explain.
b. Without measuring, write an equation for the radius of the base of the cone
you constructed in terms of the arc length you removed from the circle.
[Hint: Write an equation for the circumference of the base of the cone first.]
c. Again, without measuring, write an equation for the height of the cone you
constructed in terms of the arc length you removed from the circle.
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