Answer:
The volume of the prism is [tex]15\sqrt{3}\ units^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the prism is equal to
[tex]V=Bh[/tex]
where
B is the area of the equilateral triangle of the base
h is the height of the prism
step 1
Find the area of the base of the prism
The formula to calculate the area of a triangle by SAS (side-angle-side) is equal to
[tex]A=\frac{1}{2}(a)(b)sin(C)[/tex]
so
The area of the equilateral triangle of the base is
[tex]A=3*(\frac{1}{2}(r)(r)sin(120\°))[/tex]
we have
[tex]r=2\ units[/tex]
substitute
[tex]A=3*(\frac{1}{2}(2)(2)\frac{\sqrt{3}}{2})[/tex]
[tex]A=3\sqrt{3}\ units^{2}[/tex]
step 2
Find the volume of the prism
[tex]V=Bh[/tex]
we have
[tex]B=3\sqrt{3}\ units^{2}[/tex]
[tex]h=5\ units[/tex]
substitute
[tex]V=3\sqrt{3}*5=15\sqrt{3}\ units^{3}[/tex]
