Hexaprism container

Calculate the volume and surface in the shape of a regular hexagonal prism with a height of 1.4 m, a base edge of 3dm, and a corresponding height of 2.6 dm.

Correct answer:

V =  327.6 dm³
S =  298.8 dm²

Step-by-step explanation:

$$\begin{gathered} a=3\text{dm} \\ {v}_1=2.6\text{dm} \\ h=1.4\text{m}\to \text{dm}=1.4\cdot 10\text{dm}=14\text{dm} \\ n=6 \\ {S}_1=\frac{a\cdot v_1}{2}=\frac{3\cdot 2.6}{2}=\frac{39}{10}=3.9{\text{dm}}^2 \\ {S}_6=n\cdot S_1=n\cdot \frac{39}{10}=6\cdot 3.9=\frac{117}{5}=23.4{\text{dm}}^2 \\ V=S_6\cdot h=\frac{117}{5}\cdot h=23.4\cdot 14=\frac{1638}{5}{\text{dm}}^3=327.6{\text{dm}}^3 \end{gathered}$$

$S=2\cdot S_6+n\cdot a\cdot h=2\cdot \frac{117}{5}+n\cdot a\cdot h=2\cdot 23.4+6\cdot 3\cdot 14=298.8{\text{dm}}^2$

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