Aptitude volume and surface area

1. CUBOID

Let length = l, breadth = b and height = h units. Then

• Volume = (l x b x h) cubic units.
• Surface area = 2(lb + bh + lh) sq. units.
• Diagonal = l² + b² + h² units.
2. CUBE

Let each edge of a cube be of length a. Then,

• Volume = a³ cubic units.
• Surface area = 6a² sq. units.
• Diagonal = 3a units.
3. CYLINDER

Let radius of base = r and Height (or length) = h. Then,

• Volume = (πr²h) cubic units.
• Curved surface area = (2πrh) sq. units.
• Total surface area = 2πr(h + r) sq. units.
4. CONE

Let radius of base = r and Height = h. Then,

• Slant height, l = h² + r² units.
• Volume = (

  1 / 3

  πr²h) cubic units.
• Curved surface area = (πrl) sq. units.
• Total surface area = (πrl + πr²) sq. units.
5. SPHERE

Let the radius of the sphere be r. Then,

• Volume = (

  4 / 3

  πr³h) Cubic Units.
• Surface area = (4πr²) sq. units.
6. HEMISPHERE

Let the radius of a hemisphere be r. Then,

• Volume = (

  2 / 3

  πr³h) Cubic Units.
• Curved surface area = (2πr²) sq. units.
• Total surface area = (3πr²) sq. units.

Note: 1 litre = 1000 cm³.