Hexagonal pyramid

Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length of 3 cm and a height of 5 cm.

Correct answer:

V =  38.9711 cm³
S =  74.0951 cm²

Step-by-step explanation:

$$\begin{gathered} a=3\text{ cm } \\ h=5\text{ cm } \\ {S}_1=3\cdot \sqrt{3}\mathrm{/}2\cdot a^2=3\cdot \sqrt{3}\mathrm{/}2\cdot 3^2\doteq 23.3827{\text{cm}}^2 \\ V=S_1\cdot h\mathrm{/}3=23.3827\cdot 5\mathrm{/}3=38.9711{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} a_2=\sqrt{3}\mathrm{/}2\cdot a=\sqrt{3}\mathrm{/}2\cdot 3\doteq 2.5981\text{ cm } \\ {h}_2=\sqrt{a_2^2+h^2}=\sqrt{2.5981^2+5^2}\doteq 5.6347\text{ cm } \\ {S}_2=a\cdot h_2\mathrm{/}2=3\cdot 5.6347\mathrm{/}2\doteq 8.4521{\text{cm}}^2 \\ S=S_1+6\cdot S_2=23.3827+6\cdot 8.4521=74.0951{\text{cm}}^2 \end{gathered}$$

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