From a square plate with each side 7 cm, small squares of area 0.25 sq. cm are cut out at each corner and the remaining plate is folded up along the cuts to form an open-top cuboid. What is the volume of this cuboid (in cubic centimetres)?

Introduction / Context:
This problem describes forming an open-top box (cuboid) by cutting equal squares from the corners of a square sheet and folding up the sides. This is a standard geometry and mensuration question that tests spatial visualization and understanding of how two dimensional shapes can form three dimensional solids. The key quantities are the new base dimensions and the height of the cuboid.

Given Data / Assumptions:

• Original plate is a square with side length 7 cm.
• At each of the four corners, a small square of area 0.25 sq. cm is cut out.
• Area of each small square = 0.25 sq. cm, so side length of each small square is √0.25 = 0.5 cm.
• The plate is then folded along the cuts to create an open-top cuboid.
• The height of the cuboid is equal to the side of the small squares, that is 0.5 cm.

Concept / Approach:
When squares of side h are cut from each corner of a square with side S, the resulting base of the box has dimensions (S − 2h) by (S − 2h), and the height is h. The volume of the open-top cuboid is then volume = length * breadth * height. In this problem, S = 7 cm and h = 0.5 cm. We compute the new base side as 7 − 2 * 0.5 and then multiply by the height to get the volume.

Step-by-Step Solution:
Side length of each small square: h = √0.25 = 0.5 cm.Original square side: S = 7 cm.New base side after cutting: S − 2h = 7 − 2 * 0.5 = 7 − 1 = 6 cm.Base area of the box: 6 * 6 = 36 sq. cm.Volume of cuboid: base area * height = 36 * 0.5 = 18 cubic centimetres.

Verification / Alternative check:
To verify, note that the height cannot exceed the amount cut from each side, so 0.5 cm is consistent. Also, the base must be smaller than the original square, and 6 cm per side is 1 cm total reduction from 7 cm, consistent with cutting 0.5 cm from each end. Multiplying 36 by 0.5 again yields 18, so no arithmetic steps have been missed. This confirms the correctness of the computed volume.

Why Other Options Are Wrong:
Option 21 would require a base area or height combination that does not match the geometry of the folds. Option 16 suggests a base or height product of 4 * 4 * 1 or similar but does not match the given dimensions. Option 20 would require a slightly larger height or base, inconsistent with 0.25 sq. cm corner squares. Option 24 would correspond to a base area of 48 with height 0.5 or a base of 6 * 8, none of which arise from the given construction.

Common Pitfalls:
Students sometimes incorrectly subtract only a single h instead of 2h when finding the new base dimension, forgetting that cuts are made at both ends. Others misinterpret the given area of the small squares and assume their side is 0.25 cm instead of √0.25 cm. Miscalculating the volume by adding dimensions instead of multiplying is another typical error.

Final Answer:
The volume of the open-top cuboid formed is 18 cubic centimetres.