Answer:
[tex]\large\boxed{V=\dfrac{256\sqrt3}{3}\ cm^3}[/tex]
Step-by-step explanation:
The formula of a volume of a square pyramid:
[tex]V=\dfrac{1}{3}(b^2)(H)[/tex]
b - edge of a base
H - height
We have b = 8cm and the triangle 90 - 60 - 30. The sides of that triangle are in ptoportion 1 : √3 : 2 (look at the picture).
From the picture we have
[tex]a=\dfrac{b}{2}\to a=\dfrac{8}{2}\ cm=4\ cm[/tex]
Therefore
[tex]H=a\sqrt3\to H=4\sqrt3\ cm[/tex]
Substitute:
[tex]V=\dfrac{1}{3}(8^2)(4\sqrt3)=\dfrac{1}{3}(64)(4\sqrt3)=\dfrac{256\sqrt3}{3}\ cm^3[/tex]
