A right circular cylinder has circular cross-sectional area pi r2. Unrolling its curved surface forms a rectangle with width 2pi r and height h. **Measure** | **Formula** Volume | pi r2h Curved surface area | 2pi rh Closed total surface area | 2pi rh+2pi r2 Example A closed cylinder has radius 3 cm and height 8 cm. Its volume is 72pi cm3. Its curved area is 48pi cm2 and total surface area is 66pi cm2. With one end open, the area becomes 57pi cm2. A cylinder is not a polygonal prism, although the same “cross-sectional area x height” volume idea applies. Halve a given diameter before substituting for r.

A right circular cylinder has circular cross-sectional area \(\pi r^2\). Unrolling its curved surface forms a rectangle with width \(2\pi r\) and height \(h\).

A closed cylinder has radius 3 cm and height 8 cm. Its volume is \(72\pi\text{ cm}^3\). Its curved area is \(48\pi\text{ cm}^2\) and total surface area is \(66\pi\text{ cm}^2\). With one end open, the area becomes \(57\pi\text{ cm}^2\).

A cylinder is not a polygonal prism, although the same “cross-sectional area × height” volume idea applies. Halve a given diameter before substituting for \(r\).

Measure	Formula
Volume	\(\pi r^2h\)
Curved surface area	\(2\pi rh\)
Closed total surface area	\(2\pi rh+2\pi r^2\)

Cylinders and their nets

Cylinders and their nets