1. Cotton candy is sold at the circus in a cylindrical bucket. The height of the bucket is 13 inches, and the radius is 5.5 inches. If the bucket does not have a lid, which of the following equations represents the surface area of the cotton candy bucket? \( S A=\pi(5.5)^{2}+2 \pi(5.5)(13) \) \( S A=2 \pi(13)^{2}+2 \pi(13)(5.5) \) \( S A=2 \pi(5.5)^{2}+2 \pi(5.5)(13) \) \( S A=\pi(5.5)^{2}+\pi(5.5)(13) \)

If you want to find the surface area of a cylindrical bucket without a lid, you need to include the curved surface area and the area of the base. The formula for the surface area \( SA \) of a cylinder is given by \( SA = 2\pi r^2 + 2\pi rh \) where \( r \) is the radius and \( h \) is the height. Since the bucket is open at the top, we consider just one base. Therefore, the correct equation representing the surface area of the cotton candy bucket is \( SA = \pi(5.5)^2 + 2\pi(5.5)(13) \). Now, let's talk about some fun facts! Did you know that cotton candy was popularized at the 1904 World's Fair? It was invented by a dentist named William Morrison and a confectioner named John C. Wharton, and they even had a machine that spun sugar to create this fluffy treat! It's a staple at fairs, circuses, and carnivals, delighting kids and adults alike with its airy sweetness. Curious how concepts like this appear in real life? The engineering behind cylindrical designs is critical in various industries! For example, in packaging and manufacturing, understanding surface areas helps in optimizing materials used, minimizing waste, and ensuring the strength of containers. So, while you're munching on cotton candy, you’re actually engaging with fundamental engineering principles!