The volume of a solid is the amount of space it fills, measured in cubic units such as cm3. Prisms and cylinders share one idea: volume = area of cross-section × length. Cones and pyramids are exactly one-third of the prism or cylinder that surrounds them. Take π = 22/7.
Formulas to know
- Cube of side a: a3
- Cuboid l × w × h: lwh
- Prism: base area × length
- Cylinder r, h: πr2h
- Cone r, h: (1/3)πr2h
- Pyramid: (1/3) × base area × height
- Sphere r: (4/3)πr3
Worked example
Find the volume of a cylinder with r = 7 cm and h = 10 cm. Volume = πr2h = 22/7 × 72 × 10 = 22/7 × 49 × 10 = 22 × 7 × 10 = 1540 cm3.
Working backwards
If you know the volume you can find a missing length. A cube of volume 125 cm3 has a3 = 125, so a = 5 cm.
Key idea
Cone and pyramid volumes carry a factor of 1/3. A cone holds exactly one-third of the cylinder with the same base and height.
Remember
- Volume uses cubic units (cm3, m3).
- Prism or cylinder: cross-section area × length.
- Cone or pyramid: multiply the matching prism/cylinder by 1/3.