• A cylinder of height h, and circular base of radius r has a curved surface area of 2πrh. If it is closed, it also has two circular end faces, each of area πr². Therefore, the total surface area of a closed cylinder is 2πrh + 2πr².
• The surface area of an open-ended cylinder container will be 2πrh + 2πr².
• In general, the volume of a prism = Area of end face × Distance between the end faces. Therefore, the volume of a cylinder with radius r, and height h = πr²h.

Examples

1. A cylindrical cup has a base of radius 7 cm and a height of 10 cm. Taking the value of π to be ²²/₇, calculate :
   1. its curved surface area.
      • the area of the curved surface of a cylinder of radius r and height h is 2πrh.
      • The curved surface area of the cup = 2 × ²²/₇ × 7 × 10
      • ∴ The curved surface area of the cup = 440 cm²
   2. the area of its circular base.
      • the area of the circular base of the cup = ²²/₇ × 7 × 7
      • ∴ The area of its circular base = 154 cm²
2. How many liters can be held by a cylindrical can 14 cm in diameter and 20 cm high?
   • Volume of can = πr²h
   •                            = ²²/₇ × 7 × 7 × 20
   •                            = 3080 cm³
   • 1 liter = 1000 cm³
   • ∴ Capacity of the can = 3.08 liters.
   • The can holds about 3 liters.