Example 1
\(r = 3, h = 7 \rightarrow V = \pi(3^2)(7) = \pi(9)(7) \approx 197.92\) units³, \(SA = 2\pi(3^2) + 2\pi(3)(7) \approx 188.50\) units²
Zylinder-Rechner
Berechnen Sie Volumen und Oberfläche eines Zylinders aus Radius und Höhe mit detaillierter Schritt-für-Schritt-Lösung
Ergebnisse
Geben Sie Werte ein und klicken Sie auf Berechnen, um das Ergebnis zu sehen.
Theory & Formula
A cylinder is a three-dimensional shape with two parallel circular bases connected by a curved surface. The volume represents the amount of space inside the cylinder.
The surface area consists of two parts: the area of the two circular bases (2πr²) and the lateral surface area that wraps around the sides (2πrh). When unrolled, the lateral surface forms a rectangle with dimensions 2πr (circumference) by h (height).
Properties and Applications
- The bases are congruent circles parallel to each other
- The lateral surface area = circumference × height = 2πrh
- If the height equals the diameter (h = 2r), it's called an equilateral cylinder
- Used to calculate volumes of cans, pipes, columns, and other cylindrical objects
- A cylinder is a prism with circular bases
\(V = \pi r^2 h, SA = 2\pi r^2 + 2\pi rh\)
Worked Examples
Example 2
\(r = 5, h = 10 \rightarrow V = \pi(5^2)(10) = \pi(25)(10) \approx 785.40\) units³, \(SA = 2\pi(5^2) + 2\pi(5)(10) \approx 471.24\) units²