Final Answer:
The outer surface area of the open top cylinder can be expressed as A = 2πrₕ + πr², where r is the radius and h is the height.
Step-by-step explanation:
To calculate the outer surface area of an open top cylinder, we consider two components: the lateral surface area and the area of the circular base. The formula for the lateral surface area (the curved part) is 2πrₕ, where r is the radius and h is the height. The formula for the area of the circular base is πr², where r is the radius.
Adding these two components together gives us the total outer surface area: A = 2πrₕ + πr². The term 2πrₕ represents the surface area of the lateral side, while πr² represents the area of the circular base.
It's important to note that the open top indicates the absence of a surface covering the cylinder's top, so we do not include the area of the top circle in our calculation. The final expression A = 2πrₕ + πr² gives the outer surface area in terms of π, providing a comprehensive representation of the cylinder's surface.