A cuboid is a three-dimensional geometric shape that has six rectangular faces, where each face is a rectangle. It is also known as a rectangular prism. A cuboid has three pairs of parallel faces, and the opposite faces are equal in size and shape.

To solve problems involving a cuboid, you may need to find various measurements such as the volume, surface area, or dimensions of the cuboid. Here are some common calculations and formulas related to cuboids:

- Volume of a Cuboid: The volume (V) of a cuboid can be calculated by multiplying its length (l) by its width (w) and its height (h). The formula is: V = l × w × h.
- Surface Area of a Cuboid: The surface area (SA) of a cuboid can be calculated by finding the sum of the areas of all its faces. The formula is: SA = 2lw + 2lh + 2wh, where lw represents the area of the front and back faces, lh represents the area of the top and bottom faces, and wh represents the area of the side faces.
- Diagonal of a Cuboid: The diagonal (d) of a cuboid can be calculated using the length (l), width (w), and height (h) of the cuboid. The formula is: d = √(l^2 + w^2 + h^2).
- Finding the Dimensions: If you have the volume (V) and two out of the three dimensions (l, w, h), you can solve for the third dimension using the volume formula. For example, if you have V, l, and w, you can rearrange the volume formula to solve for h: h = V / (l × w).

When solving problems involving cuboids, make sure to identify the given information and what you are asked to find. Then apply the appropriate formula or calculation method based on the specific problem. Remember to pay attention to units of measurement and round the final answer to the appropriate degree of precision if required.

Practice problems and examples can further help in understanding how to solve specific cuboid-related questions and apply the formulas effectively.

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