Rectangular Parallelopiped or Cuboid

Multiple Choice Questions (MCQ)

1. How many faces does a cuboid have?
A. 4
B. 6
C. 8
D. 12
Answer: B. 6
2. What is the formula for the volume of a cuboid?
A. 2(lb + bh + hl)
B. l × b × h
C. 2h(l + b)
D. √(l² + b² + h²)
Answer: B. l × b × h
3. If the length = 4 cm, breadth = 3 cm, height = 5 cm, what is the Lateral Surface Area (LSA)?
A. 70 cm²
B. 60 cm²
C. 80 cm²
D. 40 cm²
Answer: C. 70 cm²
4. The diagonal of a cuboid is given by:
A. l × b × h
B. 2(lb + bh + hl)
C. 2h(l + b)
D. √(l² + b² + h²)
Answer: D. √(l² + b² + h²)
5. A box has dimensions l = 10 cm, b = 5 cm, h = 4 cm. What is its total surface area?
A. 190 cm²
B. 240 cm²
C. 280 cm²
D. 300 cm²
E. None of the above
Answer: E. None of the above

Short Answer Questions (SAQ)

1. How many edges does a cuboid have?
Answer: A cuboid has 12 edges.

2. What is the unit of volume if dimensions are in metres?
Answer: The unit of volume is cubic metres (m³).

3. Define lateral surface area of a cuboid.
Answer: Lateral Surface Area (LSA) of a cuboid is the total area of its four vertical faces, calculated using the formula LSA = 2h(l + b).

Long Answer Questions (LAQ)

1. A wooden box has dimensions: length = 1.2 m, breadth = 0.8 m, height = 0.5 m.
Find:
(a) Volume
(b) Total Surface Area
(c) Diagonal of the box
Answer: (a) Volume = l × b × h = 1.2 × 0.8 × 0.5 = 0.48 m³
(b) Total Surface Area = 2(lb + bh + hl) = 2(1.2×0.8 + 0.8×0.5 + 0.5×1.2)
= 2(0.96 + 0.4 + 0.6) = 2 × 1.96 = 3.92 m²
(c) Diagonal = √(l² + b² + h²) = √(1.44 + 0.64 + 0.25) = √2.33 ≈ 1.53 m

2. A matchbox has dimensions: length = 4 cm, breadth = 2.5 cm, height = 1.5 cm.
Calculate:
(a) Lateral Surface Area
(b) Volume
(c) Total Surface Area
Answer:
(a) Lateral Surface Area = 2h(l + b) = 2 × 1.5 × (4 + 2.5) = 3 × 6.5 = 19.5 cm²
(b) Volume = l × b × h = 4 × 2.5 × 1.5 = 15 cm³
(c) Total Surface Area = 2(lb + bh + hl) = 2(4×2.5 + 2.5×1.5 + 1.5×4)
= 2(10 + 3.75 + 6) = 2 × 19.75 = 39.5 cm²

Rectangular Parallelopiped or Cuboid