Math in the NewsIssue 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.

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

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

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

The main part of a funnel is a cone shape.

The volume of a cone is found using this formula.

Suppose the cone-shaped section of this funnel has these dimensions.

Radius = 3 in.Height = 7 in.

Here is the calculation for the volume of this funnel.

V = 1

3πr 2h

= 1

3π (3)2(7)

= 21π≈ 66 in.2

This volume of batter is converted into a cylindrical shape. But how long a cylinder would this make?

V = 1

3π r 2h

= 1

3π (3)2(7)

= 21π≈ 66 in.2

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?

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)2h

h = 66

0.0625π≈ 336 in

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.

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