We have been an image of a triangular pyramid. We are asked to find the volume of the given pyramid.
We know that volume of triangular pyramid is [tex]\frac{1}{3}b\cdot h[/tex], where,
b = Base area,
h = Height of pyramid.
We can see that base of pyramid a right triangle.
[tex]\text{Area of triangle}=\frac{1}{2}\times\text{Base}\times\text{Height}[/tex]
Now we will find height of base triangle using Pythagoras theorem.
[tex]h^2=30^2-24^2[/tex]
[tex]h^2=900-576[/tex]
[tex]h^2=324[/tex]
[tex]\sqrt{h^2}=\sqrt{324}[/tex]
[tex]h=18[/tex]
[tex]\text{Area of base triangle}=\frac{1}{2}\times24\times 18[/tex]
[tex]\text{Area of base triangle}=12\times 18[/tex]
[tex]\text{Area of base triangle}=216[/tex]
[tex]\text{Volume of triangular prism}=\frac{1}{3}b\cdot h[/tex]
[tex]\text{Volume of triangular prism}=\frac{1}{3}\cdot 216\cdot 30[/tex]
[tex]\text{Volume of triangular prism}=216\cdot 10[/tex]
[tex]\text{Volume of triangular prism}=2160[/tex]
Therefore, the volume of the given prism is [tex]2160\text{ m}^3[/tex] and option B is the correct choice.
