You cut square corners with side lengths that are whole numbers from a piece of cardboard with dimensions 20 inches by 30 inches. You then fold the cardboard to create a box with no lid. Which of the following dimensions will give you the greatest volume?

A. 12 in. by 22 in. by 4 in.
B. 10 in. by 20 in. by 5 in.
C. 14 in. by 24 in. by 2 in.
D. 10 in. by 24 in. by 6 in.
I chose D but I got it wrong :(

3 answers

after cutting out squares with sides n by n
we would have the following:
n=1 , dimensions: 18 by 26 by 1 , not given
n=2, dimensions: 16 by 26 by 2 , given incorrectly
n=3, dimensions: 14 by 24 by 3 , not given , but V =
n=4, dimensions: 12 by 22 by 4 , V = 1056
n=5, dimensions: 10 by 20 by 5 , V = 1000
n=6, dimensions: 8 by 18 by 6 , given incorrectly

of the two possibilities given correctly, the larger volume is obtained from the 12 by 22 by 4 box

I chose the A but is wrong.

I chose c and got it right