Answer:
3000
Step-by-step explanation:
Let's start by finding the volume of the wall. The volumen of the wall can be considered as the volume of a rectangular prism. The volume of a rectangular prism is given by:
![V_w=w*l*h\\\\Where:\\\\w=Width=10cm=0.1m\\l=Length=12m\\h=Height=4m](https://tex.z-dn.net/?f=V_w%3Dw%2Al%2Ah%5C%5C%5C%5CWhere%3A%5C%5C%5C%5Cw%3DWidth%3D10cm%3D0.1m%5C%5Cl%3DLength%3D12m%5C%5Ch%3DHeight%3D4m)
So the volume of the wall is:
![V_w=0.1*12*4=4.8m^3](https://tex.z-dn.net/?f=V_w%3D0.1%2A12%2A4%3D4.8m%5E3)
Now, we can find the volume of the brick using the same method since a brick can be considered as a rectangular prism as well:
![V_b=w*l*h\\\\For\hspace{3}the\hspace{3}brick\\\\w=10cm=0.1m\\l=20cm=0.2m\\h=8cm=0.08m](https://tex.z-dn.net/?f=V_b%3Dw%2Al%2Ah%5C%5C%5C%5CFor%5Chspace%7B3%7Dthe%5Chspace%7B3%7Dbrick%5C%5C%5C%5Cw%3D10cm%3D0.1m%5C%5Cl%3D20cm%3D0.2m%5C%5Ch%3D8cm%3D0.08m)
Hence:
![V_b=(0.1)*(0.2)*(0.08)=0.0016m^3](https://tex.z-dn.net/?f=V_b%3D%280.1%29%2A%280.2%29%2A%280.08%29%3D0.0016m%5E3)
In order to know how many bricks are required to build the wall, we just need to fill the wall volume with the number of bricks of this volume. So:
![V_w=nV_b\\\\Where\\\\n=Number\hspace{3}of\hspace{3}bricks](https://tex.z-dn.net/?f=V_w%3DnV_b%5C%5C%5C%5CWhere%5C%5C%5C%5Cn%3DNumber%5Chspace%7B3%7Dof%5Chspace%7B3%7Dbricks)
Solving for n:
![n=\frac{V_w}{V_b} =\frac{4.8}{0.0016} =3000](https://tex.z-dn.net/?f=n%3D%5Cfrac%7BV_w%7D%7BV_b%7D%20%3D%5Cfrac%7B4.8%7D%7B0.0016%7D%20%3D3000)
Therefore, we need 3000 bricks to build that wall.
Translation:
Comencemos por encontrar el volumen del muro. El volumen del muro puede considerarse como el volumen de un prisma rectangular. El volumen de un prisma rectangular viene dado por:
![V_w=w*l*h\\\\Donde:\\\\w=Espesor=10cm=0.1m\\l=Largo=12m\\h=Alto=4m](https://tex.z-dn.net/?f=V_w%3Dw%2Al%2Ah%5C%5C%5C%5CDonde%3A%5C%5C%5C%5Cw%3DEspesor%3D10cm%3D0.1m%5C%5Cl%3DLargo%3D12m%5C%5Ch%3DAlto%3D4m)
Entonces el volumen del muro es:
![V_w=0.1*12*4=4.8m^3](https://tex.z-dn.net/?f=V_w%3D0.1%2A12%2A4%3D4.8m%5E3)
Ahora, podemos encontrar el volumen del ladrillo utilizando el mismo método, ya que un ladrillo también puede considerarse como un prisma rectangular:
![V_b=w*l*h\\\\Para\hspace{3}el\hspace{3}ladrillo\\\\w=10cm=0.1m\\l=20cm=0.2m\\h=8cm=0.08m](https://tex.z-dn.net/?f=V_b%3Dw%2Al%2Ah%5C%5C%5C%5CPara%5Chspace%7B3%7Del%5Chspace%7B3%7Dladrillo%5C%5C%5C%5Cw%3D10cm%3D0.1m%5C%5Cl%3D20cm%3D0.2m%5C%5Ch%3D8cm%3D0.08m)
Por lo tanto:
![V_b=(0.1)*(0.2)*(0.08)=0.0016m^3](https://tex.z-dn.net/?f=V_b%3D%280.1%29%2A%280.2%29%2A%280.08%29%3D0.0016m%5E3)
Para saber cuántos ladrillos se requieren para construir el muro, solo necesitamos llenar el volumen del muro con la cantidad de ladrillos de este volumen. Entonces:
![V_w=nV_b\\\\Donde\\\\n=Numero\hspace{3}de\hspace{3}ladrillos](https://tex.z-dn.net/?f=V_w%3DnV_b%5C%5C%5C%5CDonde%5C%5C%5C%5Cn%3DNumero%5Chspace%7B3%7Dde%5Chspace%7B3%7Dladrillos)
Resolviendo para n:
![n=\frac{V_w}{V_b} =\frac{4.8}{0.0016} =3000](https://tex.z-dn.net/?f=n%3D%5Cfrac%7BV_w%7D%7BV_b%7D%20%3D%5Cfrac%7B4.8%7D%7B0.0016%7D%20%3D3000)
Por lo tanto, necesitamos 3000 ladrillos para construir ese muro.