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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.

- 3D Trigonometry Presentation A slide presentation (a poem) introducing using trigonometry (including Pythagoras' Theorem) to find lengths and angles on three dimensional shapes.
- Cylinders Apply formulae for the volumes and surface areas of cylinders to answer a wide variety of questions
- Surface Area Work out the surface areas of the given solid shapes.
- Volume Use formulae to solve problems involving the volumes of cuboids, cones, pyramids, prisms and composite solids.

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 - "
*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

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.

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