Toy cubes

From children's wooden cubes in the shape of a prism with a square base (the side of the base is 4 cm long, the height of the prism is 8 cm) a fortress is built with towers made of two cubes on top of each other ending in pyramids with the same base as the prisms and a height of 6 cm. All the walls consist of four prisms, the entrance has a lintel formed by a missing cube.

How long would the moat around the entire fortress be if we neglect its width?

How many cm³ of wood does the building contain?

Final Answer:

o =  160 cm
V =  3200 cm³

Step-by-step explanation:

$$\begin{gathered} a=4\text{cm} \\ h=8\text{cm} \\ {h}_2=6\text{cm} \\ o=4\cdot (2\cdot a+4\cdot h)=4\cdot (2\cdot 4+4\cdot 8)=160\text{cm} \end{gathered}$$

$$\begin{gathered} V_1=a^2\cdot h=4^2\cdot 8=128{\text{cm}}^3 \\ {V}_2=\frac{1}{3}\cdot a^2\cdot h_2=\frac{1}{3}\cdot 4^2\cdot 6=32{\text{cm}}^3 \\ V=4\cdot V_2+4\cdot 2\cdot V_1+4\cdot 4\cdot V_1=4\cdot 32+4\cdot 2\cdot 128+4\cdot 4\cdot 128=3200{\text{cm}}^3 \end{gathered}$$

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