Mathematics·Mensuration · NSSCO 4.3
Volume & surface area of solids
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Every box, tin, pipe, ball and cone can be measured — and this lesson shows you how, slowly and gently. We separate the two big ideas, volume (the space inside) and surface area (the skin outside), then work through the cuboid, the prism rule (area of cross-section × length), and the cylinder. Next we use the given formulae for the sphere, cone and pyramid, convert between cubic centimetres, millilitres and litres, link volume to density, and finish with a real water-tank problem in Namibian dollars.
What you'll learn in this lesson
By the end you should be able to (NSSCO Mathematics 4.3):
- Distinguish volume (cubic units) from surface area (square units) of a solid
- Find the volume and surface area of a cube and a cuboid, using its net
- Find the volume of a prism using V = area of cross-section × length
- Find the volume and surface area of a cylinder (πr²h and 2πr² + 2πrh)
- Use the given formulae for the volume of a sphere, a cone and a pyramid
- Convert between cm³, ml and litres (1 cm³ = 1 ml, 1000 cm³ = 1 litre) and link volume to density
- Solve context problems involving volume, capacity and cost in Namibian dollars
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