Brickwork volume — number of bricks for a rectangular sump wall: A rectangular sump of inner dimensions 6 m × 5 m × 4 m is to be built so that the outer dimensions are 6.2 m × 5.2 m × 4.2 m. Approximately how many bricks of size 20 cm × 10 cm × 5 cm are required for the walls (ignore mortar volume)?

Introduction / Context:
The number of bricks equals (volume of brickwork) / (volume of one brick). The brickwork volume is the difference between outer and inner rectangular prism volumes.

Given Data / Assumptions:

• Outer: 6.2 m × 5.2 m × 4.2 m
• Inner: 6 m × 5 m × 4 m
• Brick: 20 cm × 10 cm × 5 cm = 0.2 m × 0.1 m × 0.05 m
• Ignore mortar, openings, and wastage for this idealized count.

Concept / Approach:
Compute ΔV = V_outer − V_inner, then divide by V_brick.

Step-by-Step Solution:
V_outer = 6.2*5.2*4.2 = 135.408 m3V_inner = 6*5*4 = 120 m3ΔV = 15.408 m3V_brick = 0.2*0.1*0.05 = 0.001 m3Count = 15.408 / 0.001 = 15408

Verification / Alternative check:
Wall thickness implied: 0.1 m on each face; the computed ΔV matches that intuition.

Why Other Options Are Wrong:
Values differ by small offsets that do not arise from exact volume arithmetic.

Common Pitfalls:
Forgetting to convert brick dimensions from centimeters to meters; subtracting areas instead of volumes.

Final Answer:
15408