Cube & Cuboid

Important Formulas & Concepts

• Cube: A solid figure where all sides (length, breadth, height) are equal.
• Cuboid: A solid figure with different length, breadth, and height.
• Volume of Cube = a³ (where a = side length)
• Volume of Cuboid = l × b × h
• Total Surface Area of Cube = 6a²
• Total Surface Area of Cuboid = 2(lb + bh + hl)
• Lateral Surface Area of Cube = 4a²
• Lateral Surface Area of Cuboid = 2h(l + b)
• Diagonal of Cube = √3 × a
• Diagonal of Cuboid = √(l² + b² + h²)

Explanation & Examples

Example 1: Find the volume of a cube of side 5 cm.

Solution: Volume = a³ = 5³ = 125 cm³

Example 2: A cuboid has dimensions 4 cm × 5 cm × 6 cm. Find its total surface area.

Solution: TSA = 2(lb + bh + hl) = 2(20 + 30 + 24) = 2 × 74 = 148 cm²

Example 3: If the diagonal of a cube is 7√3 cm, what is the length of its side?

Solution: Diagonal = √3 × a → a = Diagonal / √3 = 7√3 / √3 = 7 cm

Previous Year Questions with Solutions

1. SSC CGL 2020: What is the volume of a cuboid of dimensions 3 cm, 4 cm, and 5 cm?
   Solution: Volume = 3 × 4 × 5 = 60 cm³
2. SSC CHSL 2019: Find the total surface area of a cube whose side is 6 cm.
   Solution: TSA = 6a² = 6 × 36 = 216 cm²
3. RRB JE 2018: A cuboid has dimensions 8 cm × 5 cm × 3 cm. Find its diagonal.
   Solution: √(8² + 5² + 3²) = √(64 + 25 + 9) = √98 = 9.89 cm
4. HSSC JE 2017: A cube has a surface area of 150 cm². Find the length of its side.
   Solution: TSA = 6a² → a² = 150/6 = 25 → a = √25 = 5 cm
5. SSC MTS 2019: Find the lateral surface area of a cuboid with dimensions 10 cm × 6 cm × 4 cm.
   Solution: LSA = 2h(l + b) = 2 × 4 × (10 + 6) = 8 × 16 = 128 cm²