Question

Consider the triangular prism below. What would be the volume of a prism that is 3 times as large?

Answer 1

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.

$\text{Base length}=3\times 3=9$

$\text{Height}=3\times 5=15$

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.

$\text{Area of base}=\frac{1}{2}\times 9\times 9$

$\text{Area of base}=\frac{1}{2}\times 81$

$\text{Area of base}=40.5$

Volume of prism would be base area times height of prism.

$V=bh$

$V=40.5\times 15$

$V=607.5$

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.