Surface Area and Volume — O/L Mathematics

What must I remember about Surface Area and Volume?

• Right circular cylinder: Curved Surface Area = 2πrh; Total Surface Area = 2πrh + 2πr² = 2πr(h + r).
• Right circular cylinder Volume: V = Base Area × Height = πr²h.
• Right prism Volume: V = Area of cross-section × length (V = A × l); Total Surface Area = (Perimeter of cross-section × length) + 2 × (Cross-sectional Area).
• Right circular cone: Volume = (1/3)πr²h; Curved Surface Area = πrl (where slant height l = √(r² + h²)).
• Sphere: Volume = (4/3)πr³; Surface Area = 4πr²; Hemisphere Volume = (2/3)πr³, Total Surface Area of solid hemisphere = 3πr².

Test yourself (1 minute)

1. Slant height vs vertical height in cone

   In curved surface area πrl, use SLANT height l; in volume (1/3)πr²h, use VERTICAL perpendicular height h.

2. Solid hemisphere total area

   Total surface area of a SOLID hemisphere includes the flat circular base: 2πr² + πr² = 3πr², NOT 2πr².

3. Volume-capacity liquid conversion

   1 litre = 1000 cm³; 1 m³ = 1000 litres; master these conversion factors for water tank problems.

Practise Surface Area and Volume questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 10, Unit 28)

What should I study first?

What comes next?

Next in the syllabus

Where does Surface Area and Volume fit in the syllabus?

Grade 10 · Term 3