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3-D shapes, volume and surface area
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Solid shapes have faces, edges and vertices. Volume measures the space inside; surface area is the total area of the outside.
Faces, edges and vertices
Faces are flat surfaces, edges are where faces meet, vertices are corners.
Volume of prisms
A prism has the same cross-section all the way through.
Volume = area of cross-section × length.
Cuboid: length × width × height. 4 × 5 × 6 = 120 cm3.
A cylinder works the same way: πr2 × height.
1 litre = 1 000 cm3.
Volume = area of cross-section × length.
Cuboid: length × width × height. 4 × 5 × 6 = 120 cm3.
A cylinder works the same way: πr2 × height.
1 litre = 1 000 cm3.
Surface area
Add the areas of all the faces. A net helps you see them.
Cuboid 3 cm × 4 cm × 5 cm: 2 × (3 × 4 + 3 × 5 + 4 × 5) = 2 × 47 = 94 cm2.
Cuboid 3 cm × 4 cm × 5 cm: 2 × (3 × 4 + 3 × 5 + 4 × 5) = 2 × 47 = 94 cm2.
A prism has a triangular cross-section with base 6 cm and height 5 cm. It is 10 cm long. Find its volume.
- Cross-section: 12 × 6 × 5 = 15 cm2
- Volume: 15 × 10
Answer: 150 cm3
Volume of any prism = area of cross-section × length. Surface area = total area of all faces. Volume is in cubic units, area in square units.
The interactive lesson includes the diagrams for this topic.
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