Final answer:
The equation to model the volume of an open-topped box made by cutting squares from each corner of a cardboard piece and folding up the flaps is V = (30 - 2x) x (70 - 2x) x x, where x represents the side length of the squares cut from each corner.
Step-by-step explanation:
To find an equation for the volume of an open-topped box made from a piece of cardboard, we must understand the impact of cutting out squares from the corners. Let's denote the side length of these squares as x inches. After removing the squares, the length and width of the resulting box will be reduced by 2x inches each (since there are two cuts made on both dimensions). Therefore, the new dimensions of the cardboard that will form the base of the box will be (30 - 2x) by (70 - 2x) inches. The height of the open-topped box will be equivalent to x inches.
The volume of the box, V, can be calculated by multiplying the length, width, and height together:
V = (length) × (width) × (height)
Substitute the new dimensions into the formula:
V = (30 - 2x) × (70 - 2x) × x
This is the equation that models the volume of the box as a function of x, the size of the cutout square.