17 a) Desenul trunchiului de piramida triunghiulara il gasesti in fisierul atasat.
17 b)
[tex] \displaystyle\\
\text{Volumul trunchiului de piramida este:}\\\\
V = \frac{h\Big(A_B + A_b + \sqrt{A_B\cdot A_b }\Big)}{3}\\\\
A_B = \text{aria bazei mari}\\
A_b = \text{aria bazei mici}\\
A_B = \frac{L^2\sqrt{3}}{4}=\frac{6^2\sqrt{3}}{4}=\frac{36\sqrt{3}}{4}=9\sqrt{3}~cm^2\\\\
A_b = \frac{l^2\sqrt{3}}{4}=\frac{4^2\sqrt{3}}{4}=\frac{16\sqrt{3}}{4}=4\sqrt{3}~cm^2\\\\
h = 9~cm [/tex]
[tex] \displaystyle\\
V = \frac{h\Big(A_B + A_b + \sqrt{A_B\cdot A_b }\Big)}{3}=\\\\
=\frac{9\Big(9\sqrt{3} + 4\sqrt{3} + \sqrt{9\sqrt{3}\cdot 4\sqrt{3} }\Big)}{3}=\\\\
=3\Big(9\sqrt{3} + 4\sqrt{3} + \sqrt{9\sqrt{3}\cdot 4\sqrt{3} }\Big)=\\\\
=3\Big(13\sqrt{3}+\sqrt{36\cdot 3}\Big)=\\\\
=3\Big(13\sqrt{3}+6\sqrt{3}\Big)=3\cdot 19\sqrt{3} = \boxed{57\sqrt{3}~cm^3}
[/tex]
