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Calculate volume, lateral surface area, and total surface area of a cylinder. Supports open and closed cylinders.
A cylinder is a 3D shape with two parallel circular bases connected by a curved surface. It's essentially a prism with a circular base, so V = Base Area × Height.
If you "unroll" the curved surface, you get a rectangle. Its width is the circumference (2πr) and its height is h. Area = 2πr × h = 2πrh.
A cylinder is a prism with a circular base. Both use the formula V = Base Area × Height. As the number of sides in a regular polygon prism increases, it approaches a cylinder.
The volume formula still works with perpendicular height. Surface area is more complex because the lateral surface is no longer a simple rectangle when unrolled.
The lateral surface area = 2πrh. This is the rectangle that wraps around the can. Add overlap for gluing.
Cans, batteries, pipes, drinking glasses, candles, tree trunks (approximately), coins (short), and cylindrical tanks.
From V = πr²h, solve for r: r = √(V/(πh)). For example, if V = 100 and h = 5, r = √(100/(5π)) = √(20/π) ≈ 2.52.