This document discusses the geometry involved in making funnel cakes at county fairs. It explains that a funnel cake starts as a cone-shaped volume of batter that is spun into a long, coiled cylindrical shape. The document calculates the volume of a sample cone-shaped funnel and finds that it would make a cylinder over 336 inches long, due to the different volume formulas for cones and cylinders.

1. Math in the News
Issue 73
County Fairs and Funnel Cakes
In this issue we look at a carnival of Geometry, as we investigate the
making of a funnel cake.

2. This YouTube video shows how funnel cakes at
your local fair are made.
http://www.youtube.com/watch?
v=3xyplVdOGoI

3. A funnel cake basically involves taking a
cone-shaped volume of batter and turning it
into a cylindrically shaped pastry.

4. Each funnel cake is made up of the long cylindrical
shape coiled into itself like a pile of string.

5. The main part of a funnel is a cone shape.

6. The volume of a cone is found using this
formula.

7. Suppose the cone-shaped section of this
funnel has these dimensions.
Radius = 3 in.
Height = 7 in.

8. Here is the calculation for the volume of
this funnel.
V =
1
3
πr 2
h
=
1
3
π(3)2
(7)
= 21π
≈ 66 in.2

9. This volume of batter is converted into a
cylindrical shape. But how long a cylinder
would this make?
V =
1
3
πr 2
h
=
1
3
π(3)2
(7)
= 21π
≈ 66 in.2

10. The volume of a cylinder is found using this
formula. Suppose that our funnel cake has
a width of 0.5 in. How long would this make
h?

11. Solving for h, we find that it would make a
336 in cylinder! Are you surprised at how
much longer it is?
66 = π(0.25)2
h
h =
66
0.0625π
≈ 336 in

12. One of the key factors to why the length of
the cylinder was so long is to look at the
volume formulas for the cone and cylinder.
For equal volumes the cylinder would be
three times longer.

13. What other factors contributed to making
the cylinder so much longer?