4side pyramid

Calculate the volume and surface of the regular four-sided pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.

Final Answer:

V =  18.48 cm³
S =  48 cm²

Step-by-step explanation:

$$\begin{gathered} a=4\text{cm} \\ \alpha =60{}^{\circ } \\ h=\frac{a}{2}\cdot \tan \alpha =\frac{a}{2}\cdot \tan 60°=\frac{4}{2}\cdot \tan 60°=\frac{4}{2}\cdot 1.732051=3.4641\text{cm} \\ {h}_2=\sqrt{h^2+(a/2{)}^2}=\sqrt{3.4641^2+(4/2{)}^2}=4\text{cm} \\ V=\frac{1}{3}\cdot a^2\cdot h=\frac{1}{3}\cdot 4^2\cdot 3.4641=18.48{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} S_1=\frac{a\cdot h_2}{2}=\frac{4\cdot 4}{2}=8{\text{cm}}^2 \\ S=4\cdot S_1+a^2=4\cdot 8+4^2=48{\text{cm}}^2 \end{gathered}$$

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