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These are the Transum resources related to the statement: "The distance between two points in three-dimensional space, and their midpoint. Volume and surface area of three-dimensional solids including right-pyramid, right cone, sphere, hemisphere and combinations of these solids. The size of an angle between two intersecting lines or between a line and a plane".

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

- Volume Video There are simple formulas that can be used to find the volumes of basic three-dimensional shapes.
- Volume Use formulae to solve problems involving the volumes of cuboids, cones, pyramids, prisms and composite solids.
- 3D Trigonometry Presentation A slide presentation (a poem) introducing using trigonometry (including Pythagoras' Theorem) to find lengths and angles on three dimensional shapes.
- Trigonometry in 3D Calculate the lengths of sides and the size of angles in three dimensional shapes.
- Cylinders Apply formulae for the volumes and surface areas of cylinders to answer a wide variety of questions
- Surface Area Video Finding the surface are of three dimensional shapes can involve some interesting formulae.
- Three Dimensional Trigonometry Video When you have mastered trigonometry in two dimensions it is time to practise solving three-dimensional problems.
- Surface Area Work out the surface areas of common solid shapes in this collection of exercises.

Here are some exam-style questions on this statement:

- "
*Twenty four spherical shaped chocolates are arranged in a box in four rows and six columns.*" ... more - "
*Rectangle ABCD is the horizontal base of a trapezoidal prism ABCDEFGH.*" ... more - "
*The diagram shows a rectangular-based pyramid, TABCD (not drawn to scale).*" ... more - "
*ABC is a triangular car park on horizontal ground. The length of AB is 90m and the length of AC is 65m. The size of angle BCA is 68*" ... more^{o}. - "
*A metal sphere has a radius 7.2 cm.*" ... more - "
*A solid metal cylinder has a base radius of 5cm and a height of 9cm.*" ... more - "
*A wedge is to be cut from a log in the shape of a cylinder as shown in the diagram below (not to scale).*" ... more

Here is an Advanced Starter on this statement:

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

The syllabus states that in problems related to these topics, students should be able to identify relevant right-angled triangles in three-dimensional objects and use them to find unknown lengths and angles.

This video on 3D shapes is from Revision Village and is aimed at students taking the IB Maths Standard level course

How do you teach this topic? Do you have any tips or suggestions for other teachers? It is always useful to receive feedback and helps make these free resources even more useful for Maths teachers anywhere in the world. Click here to enter your comments.