This worksheet extends volume and surface area skills to composite 3D objects, teaching students to combine or subtract simple solids like prisms, cylinders, cones and spheres. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- A composite object is built from two or more simple solids joined together, or one solid with a piece removed (e.g. a hole drilled through it).
- The volume of a composite object = the sum of the volumes of its parts (if joined) or the difference (if a piece is removed).
- The surface area of a composite object only counts the exposed faces — any internal face where two solids join is not part of the surface area.
- Standard volume formulas: prism V=Ah (area of cross-section × height); cylinder V=πr²h; cone V=⅓πr²h; pyramid V=⅓×base area×h; sphere V=4/3πr³; hemisphere V=2/3πr³.
- A cone's slant height (needed for its curved surface area) is found using Pythagoras' theorem: l=√(r²+h²), where h is the perpendicular height.
What your child will practise:
- Breaking a composite solid down into its simple component shapes before calculating anything.
- Adding volumes for a joined composite, or subtract for a solid with material removed.
- Identifying which faces are exposed (included in surface area) and which are internal (excluded).
- Using Pythagoras' theorem to find a cone's slant height before calculating its curved surface area.
- Converting between volume units where needed (e.g. m³ to litres, since 1 m³=1000 L).
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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