Perpendicular 79804

A perpendicular hexagonal prism was created by machining a cube with an edge length of 8 cm. The base of the prism is created from the square wall of the original cube by separating 4 identical right triangles with overhangs of lengths 3cm and 4cm. The height of the prism is 8 cm. What is the volume of a hexagonal prism

Correct answer:

V =  320 cm³

Step-by-step explanation:

$$\begin{gathered} h=8\text{cm} \\ a=8\text{cm} \\ b=3\text{cm} \\ c=4\text{cm} \\ {S}_1=a^2=8^2=64{\text{cm}}^2 \\ {S}_2=\frac{b\cdot c}{2}=\frac{3\cdot 4}{2}=6{\text{cm}}^2 \\ {S}_3=S_1-4\cdot S_2=64-4\cdot 6=40{\text{cm}}^2 \\ V=S_3\cdot h=40\cdot 8=320{\text{cm}}^3 \end{gathered}$$

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