Answer:
[tex]V=\frac{400}{3}\sqrt{3}\ cm^3[/tex]
Step-by-step explanation:
we know that
The given figure is a triangular pyramid
The volume of the triangular pyramid is equal to
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the triangular base
h is the height of the pyramid
Find the area of the base
The base is an equilateral triangle
Applying the law of sines to determine the area
[tex]B=\frac{1}{2}(10^2)sin(60^o)[/tex]
Remember that
[tex]sin(60^o)=\frac{\sqrt{3}}{2}[/tex]
substitute
[tex]B=\frac{1}{2}(10^2)\frac{\sqrt{3}}{2}[/tex]
[tex]B=25\sqrt{3}\ cm^2[/tex]
Find the volume
we have
[tex]h=16\ cm[/tex]
[tex]B=25\sqrt{3}\ cm^2[/tex]
substitute
[tex]V=\frac{1}{3}(25\sqrt{3})(16)[/tex]
[tex]V=\frac{400}{3}\sqrt{3}\ cm^3[/tex]
