For a box made by cutting corners from a sheet, model its volume as length times width times height. The cutout side becomes the height; then work out the two dimensions left on the bottom. The tempting slip is subtracting only once from a sheet dimension, even though a square is removed from each end.
Hints
- Hint 1
The height is the distance from the bottom of the box to its rim. When the remaining sides fold up, which length given by the cutout squares becomes that vertical distance?
- Hint 2
Each sheet dimension loses an -inch piece at both ends. That means you subtract twice from the original length and twice from the original width.
- Hint 3
The volume of a rectangular box is length times width times height. Multiply the three new dimensions, then set the product equal to the volume given in cubic inches.
Step-by-step
Build the box dimensions
Step 1Find the box's height
No Desmos needed. The question asks for an equation, not a value of . Folding up the sides makes each cutout square's side the box's height, so the height is inches.
- Step 2
Find the base dimensions
Each sheet dimension loses inches at both ends, so subtract from each original dimension:
- Step 3
Match the given volume
A rectangular box's volume is length times width times height. The open top doesn't change the space inside, so multiply the three dimensions and set them equal to the given volume:
- Step 4
Write the equation in the choices' form
Subtract from both sides to put zero on the left: . This equation models the box's volume of cubic inches. Choice D.