House extension

Igor is going to build an extension. He has 3 perimeter load-bearing walls: 9.1 m, 6.5 m, and 10 m long, each 3 m high. There are two windows: 2 m × 1.5 m each. How many blocks measuring 500 × 250 × 375 mm are needed to build a wall 375 mm thick? How many pallets are needed if 32 blocks fit on one pallet? Assume that blocks can be cut ideally and used without waste.

Final Answer:

n =  526.8
p =  17

Step-by-step explanation:

$$\begin{gathered} a=9.1\text{m} \\ b=6.5\text{m} \\ c=3\text{m} \\ h=0.375\text{m} \\ K=h\cdot 0.5\cdot 0.25=0.375\cdot 0.5\cdot 0.25=\frac{3}{64}\doteq 0.0469{\text{m}}^3 \\ {S}_1=2\cdot 2\cdot 1.5=6{\text{m}}^2 \\ {V}_1=S_1\cdot h=6\cdot 0.375=\frac{9}{4}=2\frac{1}{4}=2.25{\text{m}}^3 \\ {o}_1=2\cdot a+b-2\cdot h=2\cdot 9.1+6.5-2\cdot 0.375=\frac{479}{20}=23\frac{19}{20}=23.95\text{m} \\ V=o_1\cdot h\cdot c=23.95\cdot 0.375\cdot 3=\frac{4311}{160}=26\frac{151}{160}\doteq 26.9438{\text{m}}^3 \\ n=(V-V_1)/K=(26.9438-2.25)/0.0469=526.8 \end{gathered}$$

$p=\lceil n/32\rceil =\lceil 526.8/32\rceil =17$

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