After studying this section, you will be able to:

- recognise a prism as a solid with a uniform cross-section
- find the volume of a prism, a pyramid, a cone and a sphere

This video and images below explain the faces, vertices and edges of common three-dimensional shapes.

You should know and be able to use the formulae for the areas of the following shapes: parallelogram, rhombus, trapezium. These may be needed when calculating the volumes of prisms.

If a solid has a **uniform cross-section**; that is, the **cross-sectional area **is the same throughout its length then the solid is a **prism**.

You should also know the formulae for the volumes of the cone and the pyramid (although you would be given them in an examination).

**Cones and Pyramids**

- A
**cone**can be treated as a pyramid with a circular base. - The formula for the volume of a cone is the same as that for a
**pyramid**:

**Volume = 1/3 x base area x vertical height**

**Volume = 1/3****π****r ^{2}h**

*where r is the radius of the base and h is the vertical height of the cone.*

- The
**curved surface area**of a cone is given by:

**S = πrl**

where *l* is the slant height of the cone

- The
**total surface area**of a cone consists of the curved surface area plus the area of its circular base. - The total surface area is given by:

**A = ****π****rl + ****π****r ^{2}**

**KEY POINT - **The formula for the volume and curved surface area of a cone are given on the formula sheet that is included with the examination. However, it is much better to learn them.

**Spheres**

- A sphere is a ball shape.
- The Earth and other planets are approximately spherical.
- The
**volume**of a**sphere**is given by the formula:

**V = 4/3 πr^{3}**

- The
**surface area**of a**sphere**is given by the formula:

**A = 4πr ^{2}**

**Practice Question**