Question

A square tunnel was hollowed out of a triangular prism.

Answer 1

Answer:

The volume of the resulting figure is $2,240\ ft^3$

Step-by-step explanation:

step 1

Volume of the triangular prism

The volume of the prism is equal to

$V=BL$

where

B is the area of the base

L is the length of the prism

Find the area of the base B (triangular base)

$B=\frac{1}{2}(10)(12)=60\ ft^2$

$L=40\ ft$

so

$V=(60)(40)=2,400\ ft^3$

step 2

Volume of the square prism

The volume of the prism is equal to

$V=BL$

where

B is the area of the base

L is the length of the prism

Find the area of the base B (square base)

$B=2^2=4\ ft^2$

$L=40\ ft$

so

$V=(4)(40)=160\ ft^3$

step 3

Find the volume of the resulting figure

we know that

The volume of the resulting figure is equal to subtract the volume of the square prism from the volume of the triangular prism

so

$V=2,400-160=2,240\ ft^3$

Answer 2

The volume of the resulting figure is 2,240\ ft^3