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 :(
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
To find the dimensions that will give you the greatest volume, you need to calculate the volume for each option.
Let's start with option A. The dimensions are 12 in. by 22 in. by 4 in. The volume can be calculated by multiplying the three side lengths: V = 12 * 22 * 4 = 1,056 cubic inches.
Next, let's move to option B. The dimensions are 10 in. by 20 in. by 5 in. Calculate the volume using the same formula: V = 10 * 20 * 5 = 1,000 cubic inches.
Now, let's move to option C. The dimensions are 14 in. by 24 in. by 2 in. Calculate the volume: V = 14 * 24 * 2 = 672 cubic inches.
Finally, let's examine option D. The dimensions are 10 in. by 24 in. by 6 in. Calculate the volume: V = 10 * 24 * 6 = 1,440 cubic inches.
Comparing the volumes of all the options, we can see that option D has the greatest volume with a value of 1,440 cubic inches. So, your initial choice was correct and option D is the correct answer.
If you got it wrong, there might have been an error in your calculations. Please double-check your multiplication to confirm the correct answer.