Question

NEED HELP ASAP

For a piece of 3-D artwork, Eva cut a wooden block into the shape of a triangular prism with right triangle bases. She then cut a notch in the shape of a rectangular prism that runs the full 18-cm height of the block to create a solid with the dimensions shown.

What is the volume of the solid Eva created?

A. 900 cubic centimeters
B. 540 cubic centimeters
C. 1,206 cubic centimeters
D. 1,584 cubic centimeters

Answer 1

Option C.
`1,206\ cm^(3)`

Explanation:

we know that

The volume of the solid Eva created is equal to the volume of the triangular prism minus the volume of the rectangular prism notch

step 1

Find the volume of the triangular prism

The volume is equal to

`V=Bh`

where

B is the area of the triangular base

h is the height of the triangular prism

substitute

`V=(1)/(2)(12)(12)(18)=1,296\ cm^(3)`

step 2

Find the volume of the rectangular prism notch

The volume is equal to

`V=(5)(1)(18)=90\ cm^(3)`

step 3

Find the volume of the solid Eva created

`1,296\ cm^(3)-90\ cm^(3)=1,206\ cm^(3)`