Dimensions 81957

How many bricks are needed to build a wall that is 12 m long, 1.6 m high, and 47 cm wide if the dimensions of the brick are 30 x 15 x 7.5 cm and 5% of the wall volume is mortar?

Correct answer:

n =  2541

Step-by-step explanation:

$$\begin{gathered} a=12\text{m} \\ b=1.6\text{m} \\ c=47\text{cm}\to \text{m}=47:100\text{m}=0.47\text{m} \\ x=30\text{cm}\to \text{m}=30:100\text{m}=0.3\text{m} \\ y=15\text{cm}\to \text{m}=15:100\text{m}=0.15\text{m} \\ z=7.5\text{cm}\to \text{m}=7.5:100\text{m}=0.075\text{m} \\ {V}_1=a\cdot b\cdot c=12\cdot 1.6\cdot 0.47=\frac{1128}{125}=9\frac{3}{125}=9.024{\text{m}}^3 \\ r=100\%-5\%=1-\frac{5}{100}=0.95 \\ {V}_2=r\cdot V_1=0.95\cdot 9.024=\frac{5358}{625}=8\frac{358}{625}=8.5728{\text{m}}^3 \\ {V}_3=x\cdot y\cdot z=0.3\cdot 0.15\cdot 0.075=\frac{27}{8000}\doteq 0.0034{\text{m}}^3 \\ {n}_3=V_2/V_3=8.5728/0.0034\doteq 2540.0889 \\ n=\lceil n_3\rceil =\lceil 2540.0889\rceil =2541 \end{gathered}$$

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