#### 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__

__Examples__

- 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 :- 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

- 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

- the area of the circular base of the cup =

- its curved surface area.
- 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.