## Cylinders

cylinder is a prism, usually with circular ends. Most cans are cylinders.

e.g.

The cylinders we study at school are like the first one above.
It is called a right cylinder. The other one is called an oblique cylinder.

A solid cylinder is said to be closed. A hollow pipe would be an open cylinder.

There are two key measurements for a cylinder.

The height (or length), h

### Volume of a Cylinder

The volume of a cylinder uses the formula for the volume of a prism

 Volume V = (shaded area) × h V = (π r2) × h V = π r2 h

### Surface Area of a Cylinder

The surface area of a cylinder is the sum of the area of the two circular ends and the area of the curved surface.

The area of the curved surface is best seen by looking at the net of a cylinder.

 cylinder net of a cylinder Surface Area S = 2 π r 2 + 2π rh    = 2 π r(r + h)

### Examples of Cylinder Calculations

 Examples Calculation Find the volume of the cylinder below, use π = 3.1 The radius of the cylinder = 8 ÷ 2 = 4 cm V = π r2 h V = π × 42 × 12 V = 595.2 cm3 For the solid cylinder shown above, find the surface area. Surface area = 2π r2 + 2π r h Surface area = 2 × 3.1 × 42 + 2 × 3.1 × 4 × 12 Surface area = 396.8 cm2