Cylinders

Definition

A cylinder is a solid with congruent, parallel circular bases and a curved lateral surface.

Why It Matters

Cylinders are the optimal shape for containing pressurized fluids (pipes, canisters, engines) due to even stress distribution, making them ubiquitous in mechanical design.

Core Concepts

Lateral Area ( $L$ ): For a right circular cylinder, the lateral area is: $L = 2\pi rh$ $L = 2 π r h$ .
- How to read: “The lateral area L is equal to two times pi times the radius r times the height h.”
- Meaning: Area of the rolled side wall, excluding top and bottom circular bases.
Total Surface Area ( $S$ ): The sum of the lateral area and twice the base area ( $\pi r^2$ $π r^{2}$ ): $S = 2\pi rh + 2\pi r^2$ $S = 2 π r h + 2 π r^{2}$ .
- How to read: “The total surface area S is equal to two times pi times the radius r times the height h plus two times pi times the radius r squared.”
- Meaning: Total surface area of the cylinder.
Volume ( $V$ ): The product of the base area ( $\pi r^2$ $π r^{2}$ ) and the height ( $h$ $h$ ): $V = \pi r^2 h$ $V = π r^{2} h$ .
- How to read: “The volume V is equal to pi times the radius r squared times the height h.”
- Meaning: Enclosed space of the cylinder.

Definition

Why It Matters

Core Concepts

Connected Concepts

Connected notes