Surface Area of Solids — O/L Mathematics

What must I remember about Surface Area of Solids?

• Right Circular Cylinder: Curved surface area = 2πrh; Total surface area of closed cylinder = 2πrh + 2πr² = 2πr(h + r).
• Right Circular Cone: Curved surface area = πrl, where slant height l = √(r² + h²); Total surface area of closed cone = πrl + πr² = πr(l + r).
• Sphere & Hemisphere: Surface area of sphere = 4πr²; Curved surface area of hemisphere = 2πr²; Total surface area of solid hemisphere (including circular base) = 2πr² + πr² = 3πr².
• Composite Solid Surface Area: Add only the exposed external surfaces; subtract any shared contact interfaces (e.g., solid cone mounted on hemisphere: Area = πrl + 2πr²; base πr² is hidden and excluded).

Test yourself (1 minute)

1. Slant height vs Vertical height

   In cone surface area formula πrl, l MUST be the slant height l = √(r² + h²), NEVER the vertical height h.

2. Open vs Closed cylinder

   Read question carefully: Open pipe has curved surface area ONLY (2πrh); closed one end has 2πrh + πr²; closed both ends has 2πrh + 2πr².

3. Solid Hemisphere 3πr²

   Remember that a SOLID hemisphere has a flat circular base (area πr²) in addition to its curved surface (2πr²), giving total area 3πr².

Practise Surface Area of Solids questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 11, Unit 4)

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Where does Surface Area of Solids fit in the syllabus?

Grade 11 · Term 1