Question

A company is creating a box without a top from a piece of cardboard, but cutting out square corners with side length x.

Which expression can be used to determine the greatest possible volume of the cardboard box?

(x−10)(x−30)x

(10−2x)(30−2x)x

(10−x)(30−x)x

(30x−10)(10x−30)

Answer 1

(10−2x)(30−2x)x

Explanation:

I know how to explain it, but the other person's answer already has a good explanation. I'm just confirming this to be correct! :D

Answer 2

Answer: Choice B) The expression (10-2x)(30-2x)x represents the volume of the box

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The original width is 10 inches. The width reduces to 10-2x inches after we cut off the top two corners of the rectangle. We can think of it as taking 10 and subtracting off two copies of x like so: 10-x-x = 10-2x

Similarly, the length goes from 30 inches to 30-2x inches. This time we're taking off the top and bottom corners (focus on either side it doesn't matter).

The height of the box is x inches due to this portion being folded up.

Volume of box = (width)*(length)*(height)
Volume of box = (10-2x)(30-2x)x

Note: the units for the answer are in cubic inches which can be written as "in^3" (inches cubed).