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These are the Transum resources related to the statement: "Pupils should be taught to calculate surface areas and volumes of spheres, pyramids, cones and composite solids".

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.
- Surface Area Video Finding the surface are of three dimensional shapes can involve some interesting formulae.
- 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:

- "
*The diagram shows a water tank in the shape of a cylinder. It has a diameter of 76cm anf a height of 36cm.*" ... more - "
*Babatunde has to paint four containers.*" ... more - "
*The diagram show a solid cone painted two different colours.*" ... more - "
*A builder needs to lift a steel block. It is a cuboid with dimensions 2 m by 0.2 m by 0.2 m. Steel has a density of 7.6 g/cm*" ... more^{3}. - "
*[The surface area of a sphere of radius \(r\) is \(4\pi r^2\) and the volume is \(\frac43\pi r^3\)]*" ... more - "
*A circular dart board has radius of 30 cm.*" ... more - "
*The diagram, not drawn to scale, shows the plan for a large, three dimensional sign which has been ordered to hang outside an ice cream shop.*" ... more - "
*Twenty four spherical shaped chocolates are arranged in a box in four rows and six columns.*" ... more - "
*The three sides of an equilateral triangle are tangents to a circle of radius \(r\) cm. The sides of the triangle are each 10cm long.*" ... more - "
*The diagram shows a rectangular-based pyramid, TABCD (not drawn to scale).*" ... more - "
*The volume of a cone can be calculated using the formula \(V=\frac13 \pi r^2 h \) and the area of the curved surface of a cone can be calculated using \(A= \pi r l\) (where \(r\) is the radius and \(l\) is the slant height).*" ... more - "
*The diagram shows a water tank in the shape of a trapezoidal prism.*" ... more - "
*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

Here are some Advanced Starters on this statement:

**Cuboid**

Find the dimensions of a cuboid matching the description given more**Sphere Hole**

Find the volume of the remaining part of a sphere after a 10cm cylindrical hole has been drilled through it. more

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

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

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