A metallic sheet is in the shape of a rectangle with dimensions 48 m by 36 m. From each corner a square of side 8 m is cut off to make an open rectangular box. What is the volume of the box in cubic metres?

Introduction / Context:
This problem belongs to the topic of solids formed by folding metal sheets. A flat rectangular sheet is converted into an open box by cutting congruent squares from each corner and folding up the flaps. Such questions test spatial understanding and the ability to translate two dimensional dimensions into a three dimensional volume using basic geometry and mensuration formulas.

Given Data / Assumptions:
• Original sheet dimensions = 48 m by 36 m.• Squares of side 8 m are cut from each of the four corners.• An open box is formed by folding up the remaining parts.• We are asked to find the volume of this box in cubic metres.

Concept / Approach:
When a square of side 8 m is cut from each corner, the length and breadth of the base of the box are reduced by 2 times 8 m, because cuts are made at both ends along each dimension. The height of the box equals the side of the cut square, that is 8 m. Once we know the new length, breadth, and height of the box, we apply the volume formula for a cuboid, V = length * breadth * height.

Step-by-Step Solution:
Step 1: Compute the base dimensions of the box.Original length = 48 m, original breadth = 36 m.After cutting squares of side 8 m from both ends, new length = 48 − 2 * 8 = 48 − 16 = 32 m.New breadth = 36 − 2 * 8 = 36 − 16 = 20 m.Step 2: Determine the height of the box.Height = side of the cut square = 8 m.Step 3: Use the volume formula for a cuboid.V = length * breadth * height.V = 32 * 20 * 8.Step 4: Multiply step by step.32 * 20 = 640.V = 640 * 8 = 5120 cubic metres.

Verification / Alternative check:
We can check the reasonableness of the answer by noting that the original sheet area is 48 * 36 = 1728 square metres. The base of the box has area 32 * 20 = 640 square metres, which is less than the original area due to the removed corner squares. A height of 8 m gives a volume of 5120 cubic metres, which is consistent with the base area and height. There is no obvious arithmetic error in the calculations.

Why Other Options Are Wrong:
Option A: 4830 is not a product of simple integer dimensions and suggests incorrect reduction of length or breadth.Option C: 6420 is too large and would require at least one dimension to be miscomputed.Option D: 8960 assumes a larger volume than is possible with the given sheet and cut size.

Common Pitfalls:
Learners may forget that the cut happens at both ends of each side, so they subtract 8 m only once instead of twice, leading to incorrect base dimensions. Others may confuse the original sheet area with the volume, or mistakenly add instead of multiplying dimensions. Carefully drawing a sketch and systematically reducing the length and breadth by twice the cut size helps to avoid these errors.

Final Answer:
The volume of the open rectangular box is 5120 cubic metres.