We have been given a triangular prism. We are asked to find the volume of a prism that is 3 times as large.
The sides of base of triangular prism and height of new prism would be 3 times the sides and height of original prism.
[tex]\text{Base length}=3\times 3=9[/tex]
[tex]\text{Height}=3\times 5=15[/tex]
We can see that base of prism is a right triangle, so base length will be 9 and height of triangle will be 9 as well.
[tex]\text{Area of base}=\frac{1}{2}\times 9\times 9[/tex]
[tex]\text{Area of base}=\frac{1}{2}\times 81[/tex]
[tex]\text{Area of base}=40.5[/tex]
Volume of prism would be base area times height of prism.
[tex]V=bh[/tex]
[tex]V=40.5\times 15[/tex]
[tex]V=607.5[/tex]
Therefore, the volume of the prism that is 3 times as large as given prism would be 607.5 and option D is the correct choice.
