an open box is made by cutting squares from the corners of a piece of metal that is 18 cm by 26 cm. If the edge of each cut-out square is x cm, find the volume when x=1, x=2, and x=3.

If someone could explain to me how to do this. It would be very appreciated. Thanks!

take a piece of paper and scissors and actually cut out the squares, then fold up the sides

I will do the case of x = 2
then the length = 26 - 4 = 22 (cut 2 cm off each end)
the width = 18-4 = 14
the height will be 2

volume = (22)(14)(2) = 616 cm^3

do the other two cases the same way.

To find the volume of the open box, we first need to determine the dimensions of the box after the squares are cut out.

Let's start with the case when x = 1 cm.
1. First, visualize the metal piece and imagine cutting out squares of 1 cm from each corner.
2. Each corner will have a square with dimensions of 1 cm by 1 cm.
3. After cutting out the squares, the remaining piece will have dimensions of (18 - 2*1) cm by (26 - 2*1) cm.
=> Length = 16 cm; Width = 24 cm.
4. Now, the open box will have a height, h, which is the length of the side of the cut-out square. In this case, h = 1 cm.

Now that we have the dimensions, we can calculate the volume of the box.
Volume = Length * Width * Height
= 16 cm * 24 cm * 1 cm
= 384 cm³

Similarly, we can calculate the volumes for x = 2 cm and x = 3 cm.

For x = 2 cm:
1. Cut out squares of 2 cm from each corner.
2. After cutting out the squares, the remaining piece will have dimensions of (18 - 2*2) cm by (26 - 2*2) cm.
=> Length = 14 cm; Width = 22 cm.
3. The height of the open box (h) is equal to the length of the side of the cut-out square, which is 2 cm.

Volume = Length * Width * Height
= 14 cm * 22 cm * 2 cm
= 616 cm³

For x = 3 cm:
1. Cut out squares of 3 cm from each corner.
2. After cutting out the squares, the remaining piece will have dimensions of (18 - 2*3) cm by (26 - 2*3) cm.
=> Length = 12 cm; Width = 20 cm.
3. The height of the open box (h) is equal to the length of the side of the cut-out square, which is 3 cm.

Volume = Length * Width * Height
= 12 cm * 20 cm * 3 cm
= 720 cm³

So, the volumes of the open box when x = 1, 2, and 3 cm are 384 cm³, 616 cm³, and 720 cm³, respectively.