Actually, they work for two different reasons. First, they direct your voice. As sound emerges from your mouth, it travels outward in all directions, going left, right, up, and down, as well as straight ahead. Using a megaphone is a lot like using a funnel--it directs more sound toward your target, and allows less to scatter to the sides.

This is only half the story, though. Megaphones don't simply aim the sound that you're already making, they can actually draw more volume from your mouth in the first place. This is because whenever a sound wave moves suddenly from a narrow space to a more open one, some of the sound is reflected backward. This is exactly what happens when the sound of your voice moves from the narrow confines of your mouth into the wide, open air. The abrupt change bounces some of the sound energy backward, where it's absorbed by your mouth, reducing the overall volume.

A cone shaped megaphone creates a more gradual transition from your mouth to the open air. By reducing the amount of sound that bounces back into your mouth, this allows more volume to come out. For full effect, a megaphone should be at least as long as the wavelength of the sound it's amplifying. Human voices have wavelengths up to several feet long, so a professional megaphone, like a cheerleader might use, is also several feet long.