From each corner of a rectangular sheet of cardboard with dimensions 25 cm by 20 cm, a square of side 2 cm is cut out and the sides are folded up to form an open box. What is the volume of the resulting box in cubic centimetres?

Introduction:
This is a classic mensuration problem about forming an open-top box from a rectangular sheet by cutting squares from each corner. You need to understand how the dimensions of the box change after the cuts and folds, and then apply the volume formula for a rectangular prism (cuboid).

Given Data / Assumptions:

• Original rectangle dimensions: length = 25 cm, breadth = 20 cm.
• Squares of side 2 cm are cut from each of the four corners.
• These flaps are folded up to form an open box.
• The box is rectangular with height equal to the side of the cut-out square.
• We need the volume of the box in cm³.

Concept / Approach:
When a square of side 2 cm is cut from each corner and the sides are folded up, the height of the box is 2 cm. The length and breadth of the base of the box are reduced by twice the cut-out size, because squares are removed from both ends. Once the new length, new breadth, and height are known, volume = length * breadth * height.

Step-by-Step Solution:
Step 1: Determine the new base dimensions.Original length = 25 cm. Squares of 2 cm are cut from both ends, so new length = 25 − 2 − 2 = 21 cm.Original breadth = 20 cm. Squares of 2 cm are cut from both ends, so new breadth = 20 − 2 − 2 = 16 cm.Height of the box = 2 cm (equal to side of square cut).Step 2: Compute the volume.Volume = length * breadth * height = 21 * 16 * 2.First, 21 * 16 = 336.Then 336 * 2 = 672 cm³.

Verification / Alternative check:
Visualising the net of the box helps: the central rectangle that becomes the base is 21 by 16, and the four 2 cm high side rectangles fold up as walls. Since none of the material is wasted beyond the corner squares, the dimensions above are consistent. Recomputing quickly shows the same result: 21 * 16 = 336, and times 2 gives 672 cm³.

Why Other Options Are Wrong:
828 cm³ or 1000 cm³ would require larger base dimensions or height, which do not match the cut size. 500 cm³ and 600 cm³ are simply wrong volumes based on incorrect dimension reductions or arithmetic mistakes. Only 672 cm³ follows correctly from the geometry of cutting 2 cm squares from each corner.

Common Pitfalls:
Common errors include subtracting 2 cm only once from length and breadth, forgetting that the cutouts occur on both sides. Another mistake is to misidentify the height of the box, taking the original sheet thickness instead of the square side length. Careful visualisation and stepwise deduction avoid these issues.

Final Answer:
The volume of the box formed from the rectangular sheet is 672 cm³.