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Materials: 10 m³ brick 1:4, 100 m³ PCC 1:3:6

Short answer

For 10 m3 brickwork in 1:4, using 230x110x55 mm bricks with joints: bricks 5,342, cement 18.8 bags, sand 2.61 m3. For 100 m3 PCC 1:3:6, dry volume 154 m3: cement 443.5 bags, sand 46.2 m3, coarse aggregate 92.4 m3.

Calculate the quantities of materials required for i) 10 m³ brick masonry in 1:4 cement mortar ii) 100 m³ PCC 1:3:6 in foundation.

Assumptions: dry volume = 1.54 × wet volume for concrete and 1.27 × wet volume for mortar; 1 m³ of cement = 28.8 bags. The brick size is not given, so 230 × 110 × 55 mm bricks with 10 mm joints are assumed.

(i) 10 m³ brickwork in 1:4 cement mortar

  • Volume of one brick with mortar =0.240×0.120×0.065=1872.0×10−6= 0.240 \times 0.120 \times 0.065 = 1872.0\times 10^{-6} m³; bricks per m³ =1/(1872.0×10−6)=534.19= 1/(1872.0\times10^{-6}) = 534.19
  • Bricks for 10.00 m³ =534.19×10.00=5,342= 534.19 \times 10.00 = 5,342 nos
  • Volume of one brick alone =0.230×0.110×0.055=1391.5×10−6= 0.230\times0.110\times0.055 = 1391.5\times10^{-6} m³; wet mortar per m³ =1−534.19×1391.5×10−6=0.2567= 1 - 534.19\times1391.5\times10^{-6} = 0.2567 m³
  • Wet mortar for 10.00 m³ =2.567= 2.567 m³; dry volume =1.27×2.567=3.260= 1.27\times2.567 = 3.260 m³
  • Cement =1/5×3.260=0.652= 1/5\times3.260 = 0.652 m³ =0.652×28.8=18.8= 0.652 \times 28.8 = 18.8 bags
  • Sand =4/5×3.260=2.608= 4/5\times3.260 = 2.608 m³

(ii) 100 m³ PCC (1:3:6) in foundation

  • Wet volume =100.000= 100.000 m³; dry volume =1.54×100.000=154.000= 1.54 \times 100.000 = 154.000 m³ (sum of ratio =1+3+6=10= 1 + 3 + 6 = 10)
  • Cement =1/10×154.000=15.400= 1/10 \times 154.000 = 15.400 m³ =15.400×28.8=443.5= 15.400 \times 28.8 = 443.5 bags (50 kg)
  • Sand =3/10×154.000=46.200= 3/10 \times 154.000 = 46.200 m³
  • Coarse aggregate =6/10×154.000=92.400= 6/10 \times 154.000 = 92.400 m³

Answer: (i) bricks 5,342 nos, cement 18.8 bags, sand 2.61 m³. (ii) cement 443.5 bags, sand 46.20 m³, coarse aggregate 92.40 m³.

✓ Answer checked by Claude Opus 5.5 (high effort)

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