Volume of Solids — O/L Mathematics

What must I remember about Volume of Solids?

• Uniform Prism Volume: Volume = Cross-sectional Area × Length = A × L (e.g., Cuboid V = l × b × h; Triangular prism V = (1/2) b h × L).
• Right Circular Cylinder: Volume = Base Area × Height = πr²h.
• Right Circular Cone: Volume = (1/3) × Base Area × Height = (1/3)πr²h; cone volume is exactly one-third the volume of a cylinder of identical base radius and height.
• Sphere & Hemisphere: Volume of sphere = (4/3)πr³; Volume of hemisphere = (2/3)πr³; Pyramid volume = (1/3) × Base Area × Perpendicular Height.

Test yourself (1 minute)

1. Melting and Recasting Conservation

   When a solid is melted and recast into a different shape (e.g., metal sphere melted into cylinder or small spheres), TOTAL VOLUME REMAINS STRICTLY CONSERVED: V_initial = V_final.

2. Volume of Hollow Shells

   Volume of material in hollow cylinder = π(R² - r²)h; Volume of material in hollow sphere = (4/3)π(R³ - r³).

3. Logarithmic calculation in volume

   Paper 2 Part B volume questions frequently require solving volume formulas using four-figure logarithm tables; maintain characteristics correctly.

Practise Volume of Solids questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 11, Unit 5)

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Where does Volume of Solids fit in the syllabus?

Grade 11 · Term 1