A solid cuboid of dimensions 50 cm × 40 cm × 30 cm is cut into 8 identical smaller cuboids by making 3 cuts, each cut parallel to one of its faces. What is the total surface area, in square centimetres, of all the 8 smaller cuboids together?

Introduction / Context:
This problem tests understanding of how cutting a solid affects total surface area. A large cuboid is divided into smaller identical cuboids by planes parallel to its faces. Although the total volume remains the same, new internal faces become external surfaces of the smaller pieces, which changes the sum of their surface areas. Such questions are common in aptitude exams because they involve both geometry and spatial reasoning.

Given Data / Assumptions:

Original cuboid dimensions: 50 cm, 40 cm and 30 cm.
The cuboid is cut into 8 identical smaller cuboids.
Three cuts are made, each parallel to a face, so that the three dimensions are each divided by 2.
No material is lost in cutting.
We must find the total surface area of all 8 smaller cuboids combined.

Concept / Approach:
To obtain 8 equal parts from a cuboid, one cut is made along each dimension, halving length, breadth and height. This yields smaller cuboids with dimensions equal to half of each original dimension. The surface area of a cuboid with dimensions l, b and h is given by 2 * (l * b + b * h + h * l). First, determine the dimensions of each smaller cuboid and compute its surface area. Then multiply by 8 for the total surface area of all parts.

Step-by-Step Solution:
Original dimensions: length L = 50 cm, breadth B = 40 cm, height H = 30 cm. To get 8 parts, each dimension is halved: L is cut into two segments of 25 cm, B into two segments of 20 cm, and H into two segments of 15 cm. So each small cuboid has dimensions: l = 25 cm, b = 20 cm, h = 15 cm. Surface area of one small cuboid: S_one = 2 * (l * b + b * h + h * l). Compute products: l * b = 25 * 20 = 500; b * h = 20 * 15 = 300; h * l = 15 * 25 = 375. Sum inside brackets: 500 + 300 + 375 = 1175. S_one = 2 * 1175 = 2350 square centimetres. There are 8 identical cuboids, so total surface area S_total = 8 * 2350 = 18800 square centimetres.

Verification / Alternative check:
We can compare with the surface area of the original cuboid. Original surface area S_original = 2 * (50 * 40 + 40 * 30 + 30 * 50) = 2 * (2000 + 1200 + 1500) = 2 * 4700 = 9400 square centimetres. After cutting, the total surface area 18800 is exactly double. This makes sense because new faces appear inside the original cuboid that become external surfaces of the smaller pieces, increasing the overall surface area.

Why Other Options Are Wrong:
11750 and 14100 correspond to miscalculations where one or two face products are omitted or not doubled correctly.
23500 would arise if you mistakenly took the surface area of one small cuboid as the total or miscounted the number of parts.
16400 is another incorrect intermediate value that does not match any consistent application of the surface area formula and the number of pieces.

Common Pitfalls:
Learners sometimes assume the total surface area remains unchanged after cutting, which is true for volume but not for surface area. Another mistake is to divide the original surface area by 8 instead of recalculating for each smaller cuboid. Misapplying the formula for surface area and confusing l, b and h values also leads to errors. It is important to recompute based on the new dimensions and then multiply by the correct number of identical parts.

Final Answer:
The total surface area of all the 8 smaller cuboids is 18800 square centimetres.