How many cubes with side lengths of 1 3 cm 3 1 cmstart fraction, 1, divided by, 3, end fraction, start text, space, c, m, end text does it take to fill the prism?

Step-by-step explanation:

Given that the length of the prism is cm, and  it is made up of eight cm cubes

The width is cm, so it is made up 3 rows of cm cubes

That means the bottom layer of cubes is made up of 3 rows of 8 cubes

∴ the bottom layer is made of 24 cubes

The height is cm, so it is made up of 2 layers of cm cubes.

So there are 2 layers of 24 cubes

∴ 48 cubes takes to fill the given prism.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.