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