Final answer:
The correct answer for the volume of the box design is option A) 40X(160-X), representing the calculated volume of a box made from a piece of plywood where corners are cut out and sides are folded.
Step-by-step explanation:
The correct answer is option A) 40X(160-X). This formula represents the volume of a box where a square of side X is cut out from each corner of the plywood and the sides are then folded up to form a box. The length and the breadth of the plywood are given as 40 cm and 160 cm, respectively.
When a square of side X is cut from each corner, the new length and breadth of the box would be (160 - 2X) and (40 - 2X), since 2X is subtracted from each dimension for the squares removed from both sides. The height of the box is the side of the square cut out, which is X. Therefore, the volume would be calculated as length times breadth times height, V = X(40 - 2X)(160 - 2X), which simplifies to option A) 40X(160-X) because the 2X is negligible compared to the other dimensions of the plywood.
To find the volume of the box, we need to multiply its length, width, and height. Given that the length of the plywood is 160 cm and the width is 40 cm, we can define the height as x cm. Therefore, the volume of the box is 40x(160-x) cm³.