# 3.1 Volume and surface area

## 3D Shapes

This section is all about the volume and surface area of prisms, cylinders, pyramids, cones and spheres! All of these shapes has their own unique properties and this section is about understanding and calculating the volumes and surface areas.

Key Concepts

In this unit you should learn to…

• work out the volume and surface area of 3 shapes including prisms, cylinders, pyramids, cones and spheres

• Use the above to solve problems in 3 dimensions

Essentials

Slides Gallery - Part 1 - Prisms

1.  What are Prisms

This is a video explaining the properties of a prism and looking at different kinds of prism.

2. Volume of Prisms

Here we learn about how to use the properties of prisms to calculate their volumes. the video goes through some examples.

3.Surface area of prisms

Here we learn about calculating surface area by examining the nets of different kinds of prisms.

Volume and Surface area of Cylinders

Here are some slides and videos going over cylinders. Cylinders have the same properties as Prisms, but because the cross section is a circle which is not a straight edge there is a bit of extra thinking to do.

4.  Volume of Cylinders

Here we look at applying the same principles as with prisms to cylinders with their circular base.

5. Surface area of cylinders

The nets of cylinders just take a little bit more thought.....

Pyramids and Cones

This section of the page moves on to pyramids and their properties. We will look at calculating their respective volumes and surface areas.

6. What are pyramids?

Defining the key properties of these shapes and looking at a few different ones.

7. Volume of a pyramid and cone

This is calculated by taking a third of the volume of the prism it would fit in. This video shows this in action.

8. Surface area of a Pyramid

Here we look at the nets of different pyramids so we can see how surface area can be calculated.

Cones and Spheres

In this last section we deal with these shapes with curved surface areas, their properties, volume and surface area

9. Surface Area of a Cone

Unpacking the net of a cone is lovely example of mathematical links. In this video, we explore the links between the variables and show how to calculate this.

10. Volume and Surface area of a Sphere

The sphere is in one way the hardest to deal with, but in another can be done with some startlingly simple formulae!

Summary

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Test Yourself