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?
A.) (15−x)(22−x)x
B.) (x−15)(x−22)x
C.) (15−2x)(22−2x)x
D.) (22x−15)(15x−22)
+9466 volume of box = (width)(length)(height)
width = 15 - x - x
width = 15 - 2x
length = 22 - x - x
length = 22 - 2x
height = x
volume of box = (width)(length)(height)
volume of box = (15 - 2x)(22 - 2x)x
The expression (15 - 2x)(22 - 2x)x can be used to determine the volume of the box.
( And by looking at a graph we can see that the greatest possible volume is about 432 in3 .
Here's a graph: https://www.desmos.com/calculator/h7gylso5p9
And note that the length of x can't actually be greater than 15/2 in. )
+9466 volume of box = (width)(length)(height)
width = 15 - x - x
width = 15 - 2x
length = 22 - x - x
length = 22 - 2x
height = x
volume of box = (width)(length)(height)
volume of box = (15 - 2x)(22 - 2x)x
The expression (15 - 2x)(22 - 2x)x can be used to determine the volume of the box.
( And by looking at a graph we can see that the greatest possible volume is about 432 in3 .
Here's a graph: https://www.desmos.com/calculator/h7gylso5p9
And note that the length of x can't actually be greater than 15/2 in. )
