Question

HELP ASAP!! could someone help me figure out the pattern? it’s due tomorrow!!

Answer 1

Answer:

See attached image

Step-by-step explanation:

If we cut off a square from each corner of a sheet of paper of size (L x W =11" x 8") and each square has a side of a" then overall length and width are each reduced by 2a"

The height is the same as the square side

So for each entry, subtract 2 x side length from both the height and width and then compute the volume.

See attached image for solution

IMPORTANT NOTES
The general rule for computing length and width for a cutout of side x is

Length = 11 - 2x, Width = 8.5 - 2x and Height =x

This is the last row in the table

The volume would be
( 11 - 2x) (8.5 - 2x) (x) = 4x³ -  39x² + 93.5x

!!!Some of the already filled-in entries appear to be incorrect!!
The filled in numbers relating to Width for cut-out size of 3 inches and 4 inches do not follow the above pattern. Everything else looks OK. You may want to check your calculations. These affect the volume also. I have indicated these by putting two question marks in red

For cutout = 3 in, Length = 5 and height = 3 (both OK but width should be 8.5 - 2 x 3 = 8.5 - 6 = 2.5.
Then volume = 5 x 2.5 x 3 = 37.5 in³

For cutout = 4 in, Length = 3 and height = 4 (both OK but width should be
8.5 - 2 x 4 = 8.5 - 8 = 0.5 in
Volume = 3 x 0.5 x 4 = 6 in³

Please double-check these two row entries for width and volume. Or ask your teacher if he/she already filled them in for you.

I cannot find a logical reason for these two width values being inconsistent with the rest of the values for width

Hope that helps