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A square tunnel was hollowed out of a triangular prism.

A square prism inside of a larger triangular prism. The square prism has a length of 2 feet, with of 40 feet, and height of 2 feet. The triangular prism has triangular sides with a base of 10 feet, height of 12 feet, and side lengths of 13 feet. The prism has a height of 40 feet.

Complete the work to find the volume of the resulting figure.

Volume of the triangular prism

V = Bh

V = 1
2
(10)(12)(40) = 2,400 ft3

Volume of the square prism

V = Bh

V = (22)(40) = 160 ft3

The volume of the resulting figure is
ft3.

A square tunnel was hollowed out of a triangular prism A square prism inside of a larger triangular prism The square prism has a length of 2 feet with of 40 fee class=

Respuesta :

calculista

Answer:

The volume of the resulting figure is [tex]2,240\ ft^3[/tex]

Step-by-step explanation:

step 1

Volume of the triangular prism

The volume of the prism is equal to

[tex]V=BL[/tex]

where

B is the area of the base

L is the length of the prism

Find the area of the base B (triangular base)

[tex]B=\frac{1}{2}(10)(12)=60\ ft^2[/tex]

[tex]L=40\ ft[/tex]

so

[tex]V=(60)(40)=2,400\ ft^3[/tex]

step 2

Volume of the square prism

The volume of the prism is equal to

[tex]V=BL[/tex]

where

B is the area of the base

L is the length of the prism

Find the area of the base B (square base)

[tex]B=2^2=4\ ft^2[/tex]

[tex]L=40\ ft[/tex]

so

[tex]V=(4)(40)=160\ ft^3[/tex]

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

[tex]V=2,400-160=2,240\ ft^3[/tex]

alyssa2481

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

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