A cylinder is a box’s round cousin: a circle extruded to a height h. Its volume is the base-circle area times the height, V = πr²h — literally "area of the circle, stacked h high". The curved side, if unrolled, is a rectangle of width equal to the circumference (2πr) and height h, giving a lateral surface area of 2πrh. Add the two circular ends (each πr²) for the total surface area, 2πr² + 2πrh. As with circles, keep answers in terms of π and be careful whether the problem states the radius or the diameter — halve the diameter first. Reverse questions divide the volume by πr² (or by 2πr for lateral area) to recover a missing height.
✅ Solved examples
1. A cylinder has a radius of 3 and a height of 5. Find its volume.
V = πr²h = π × 3² × 5 = π × 9 × 5 = 45π.
2. A cylinder has a diameter of 10 and a height of 4. Find its volume.
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