Volume of Cylinder Calculator
Volume
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Lateral Surface Area
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Total Surface Area
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How to Calculate the Volume of a Cylinder
A cylinder's volume is calculated with V = πr²h, where r is the radius of the circular base and h is the height. This formula works by multiplying the area of the circular base (πr²) by the height. It applies to right circular cylinders — the most common type.
The lateral surface area is the area of the curved side: LSA = 2πrh. Think of it as unrolling the cylinder into a rectangle. The total surface area includes both circular ends: TSA = 2πr(r + h). These are important for calculating material costs for tanks, cans, and pipes.
Cylinders appear throughout daily life — beverage cans, water tanks, pipes, and silos. Knowing the volume helps determine capacity, while surface area is essential for coating, insulation, and manufacturing cost estimation.
Frequently Asked Questions
What is the volume formula for a cylinder?
Volume = πr²h, where r is the radius and h is the height. A cylinder with radius 3 and height 10 has volume ≈ 282.74 cubic units.
How do you find the surface area of a cylinder?
Total surface area = 2πr(r + h). This includes the two circular bases and the curved lateral surface.
What is the lateral surface area?
The lateral surface area is just the curved side: LSA = 2πrh. If you unrolled it flat, it would form a rectangle with width = circumference and height = cylinder height.
How do you find the volume of a half cylinder?
Divide the full cylinder volume by 2: V = πr²h / 2. This gives the volume of a semicircular trough or half-pipe shape.