Find the number of bricks, each measuring 54 cm × 16 cm × 82 cm, required to…
2026
Find the number of bricks, each measuring 54 cm × 16 cm × 82 cm, required to construct a wall 82 m long, 51 m high and 0.9 m thick, if the sand and cement mixture occupies 60% of the total volume of the wall.
Answer: D. 21250 — Concept — When identical solid blocks fill a region and a fixed fraction of that region is taken up by something else, the blocks can occupy only the…
- A.
21400
- B.
21200
- C.
21000
- D.
21250
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Correct answer: D
Concept — When identical solid blocks fill a region and a fixed fraction of that region is taken up by something else, the blocks can occupy only the remaining fraction of the total volume. The number of blocks is therefore (volume left for the blocks) divided by (volume of one block). Before the two volumes are compared, every length must be expressed in the same unit.
Applying this to the given wall:
Volume of the wall = 82 m × 51 m × 0.9 m = 3763.8 m3.
The sand and cement mixture takes 60% of this volume, so the bricks take the remaining 40%: 0.40 × 3763.8 = 1505.52 m3.
Express one brick's edges in metres: 54 cm = 0.54 m, 16 cm = 0.16 m and 82 cm = 0.82 m.
Volume of one brick = 0.54 m × 0.16 m × 0.82 m = 0.070848 m3.
Number of bricks = 1505.52 ÷ 0.070848 = 21250.
Cross-check — 21250 × 0.070848 = 1505.52 m3, and 1505.52 ÷ 3763.8 = 0.40 exactly. So the bricks account for 40% of the wall's volume and the mixture for the stated 60%, which matches the condition given in the question.