Geometry - Cuboid

Cuboid

Understanding Cuboid in Geometry: Definition, Properties, and Key Formulas

A cuboid is a three-dimensional geometric shape with six rectangular faces. It is one of the most common 3D shapes encountered in daily life, resembling objects like boxes, bricks, and rooms. A cuboid is characterized by its length (\(l\)), width(\(w\)) and height (\(h\)) which form its dimensions.

Diagram of a cuboid with labeled dimensions: length, width, and height.

Key Properties of a Cuboid

  1. Faces: A cuboid has six rectangular faces. Opposite faces are identical in size and shape.
  2. Edges: It has 12 edges, where opposite edges are equal in length.
  3. Vertices: A cuboid has 8 vertices, which are the points where the edges meet.
  4. Shape: All angles in a cuboid are \(90 ^\circ \) , making it a rectangular prism.

Key Formulas for a Cuboid

1. Volume \(V\)

The volume of a cuboid measures the space it occupies:

\[ V = lwh \]

where:

  • \(l\): length
  • \(w\): width
  • \(h\): height

2. Surface Area \(A\)

The surface area is the total area of all six faces of the cuboid:

\[ A = 2 (lw + wh + hl) \]

This formula sums the areas of each pair of opposite rectangular faces.

Applications of Cuboids

  • Daily Life: Cuboids are used to model everyday objects like shipping boxes, bricks, and rooms.
  • Architecture and Design: Essential for calculating material requirements and space utilization.
  • Engineering: Used to study structural integrity and object placement in 3D space.
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