How to Calculate the Volume of a Cylinder
This calculator determines the volume, lateral surface area, total surface area, and base area of a cylinder from the base radius and height.
Cylinder Formulas
The cylinder is a solid of revolution obtained by rotating a rectangle around one of its sides. The fundamental formulas are:
- Volume: V = pi x r² x h
- Lateral surface area: S_lat = 2pi x r x h
- Total surface area: S_tot = 2pi x r x (r + h)
- Base area: A_base = pi x r²
Where r is the base circle radius and h is the cylinder height.
Understanding the Formulas Intuitively
The volume of a cylinder is simply the base area multiplied by the height -- like stacking infinitely many circles on top of each other. This is the same principle that applies to any prism.
The lateral surface area becomes intuitive if you imagine cutting the cylinder vertically and unrolling it: you get a rectangle whose base is the circumference of the circle (2pir) and whose height is h. Therefore S_lat = 2pir x h.
Practical Applications
The cylinder is one of the most common geometric shapes in everyday objects: cans and barrels for calculating capacity, columns and pillars in construction, pistons and hydraulic cylinders in engineering, and storage tanks in the food industry.
Useful Conversions
Remember that 1 liter = 1,000 cm³ = 1 dm³. So a cylinder with r = 5 cm and h = 10 cm has volume V = pi x 25 x 10 = approximately 785.4 cm³ = approximately 0.785 liters. This conversion is essential when working with liquids.