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Cylinder - Area and Volume

  • 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.
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