The length, breadth and height of a solid cuboid are 12 centimetres, 8 centimetres and 6 centimetres respectively. What is the volume of this cuboid in cubic centimetres?

Introduction / Context:
This is a straightforward mensuration question about the volume of a rectangular cuboid. The three dimensions of the cuboid are provided and we must compute the volume. Although the original statement mentions a value for pi, pi is not required here because a cuboid involves only straight edges and right angles, not circular shapes. This question tests basic understanding of volume formulas in three dimensional geometry.

Given Data / Assumptions:

• Length of the cuboid L = 12 cm.
• Breadth (width) of the cuboid B = 8 cm.
• Height of the cuboid H = 6 cm.
• We are asked to find the volume in cubic centimetres.
• The cuboid is a rectangular box, so all angles are right angles.

Concept / Approach:
The volume of a cuboid is given by:
V = L * B * H,
where L is length, B is breadth and H is height. Since all measurements are in the same unit (centimetres), we simply multiply these three numbers to obtain the volume in cubic centimetres. No circular geometry is involved, so pi is irrelevant despite being mentioned in the original text.

Step-by-Step Solution:
Step 1: Write down the formula for volume of a cuboid: V = L * B * H. Step 2: Substitute the given values: L = 12 cm, B = 8 cm, H = 6 cm. Step 3: Compute L * B = 12 * 8 = 96. Step 4: Multiply by the height: V = 96 * 6 = 576. Step 5: Therefore, the volume V = 576 cubic centimetres.

Verification / Alternative check:
We can cross check by arranging factors differently: 12 * 6 = 72, and 72 * 8 = 576, which matches the previous calculation. Since all three dimensions are positive and the multiplication is straightforward, there is no ambiguity in the result. The unit is cubic centimetres because we multiplied centimetres three times (cm * cm * cm).

Why Other Options Are Wrong:
288 cubic centimetres and 432 cubic centimetres result from mistakenly multiplying only two of the three dimensions or from arithmetic errors. 864 cubic centimetres and 1152 cubic centimetres come from overestimating one of the products, for example treating one dimension as 12 instead of 6 or multiplying incorrectly. Only 576 cubic centimetres correctly reflects the product 12 * 8 * 6.

Common Pitfalls:
Students sometimes confuse surface area with volume and try to add terms like 2(LB + BH + LH), which is incorrect for volume. Another pitfall is mixing units or thinking pi is involved simply because it is written in the question. Remember that volume for a cuboid always comes from multiplying the three orthogonal edge lengths using consistent units, without any involvement of pi.

Final Answer:
The volume of the cuboid is 576 cubic centimetres.