Surface Area and Volume (Copy)

Cheat Sheet: Surface Area and Volume of Solids (IGCSE Mathematics 0580 – CORE)
Topic: Cuboid, Prism, Cylinder, Sphere, Pyramid, Cone

1. Cuboid

• Surface Area = 2(lb + bh + hl)
  (l = length, b = breadth/width, h = height)
• Volume = length × width × height

2. Prism (Any solid with uniform cross-section)

• Surface Area = (Perimeter of cross-section × length) + (2 × area of cross-section)
• Volume = area of cross-section × length

3. Cylinder

• Curved Surface Area = 2πrh
  (r = radius, h = height)
• Total Surface Area = 2πrh + 2πr²
  (curved area + areas of two circular ends)
• Volume = πr²h

4. Sphere

• Surface Area = 4πr²
• Volume = (4/3)πr³

5. Pyramid

• Surface Area = (area of base) + (sum of areas of triangular faces)
• Volume = (1/3) × area of base × height

6. Cone

• Curved Surface Area = πrl
  (r = radius, l = slant height)
• Total Surface Area = πrl + πr²
  (curved area + base area)
• Volume = (1/3)πr²h
  (h = vertical height)

7. Important Notes

• If the question asks for the answer in terms of π, leave π in the answer.
• For cones, l is the slant height and h is the vertical height.
• For prisms, cross-section must be identified first (e.g., triangle, rectangle, semicircle).

8. Quick Reference Table

This cheat sheet fully covers CORE-level formulas and methods for solving surface area and volume problems for cuboids, prisms, cylinders, spheres, pyramids, and cones.