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We notice various items in our daily lives, such as notebooks, matchboxes, instrumental geometry boxes, cones, cricket balls, cylinders, and so on. All of these things are three-dimensional (solid shapes). All of these objects have three dimensions: length, breadth, height, and depth.
Furthermore, we frequently come across shapes that have two or more identical (congruent) faces. The Cube, for example, has squared faces on each side, but the Cuboid has rectangular faces.
A three-dimensional form having six faces, eight vertices, and twelve edges is known as a Cube or Cuboid. The major difference between a cube and a cuboid is that a cube has the same length, width, and height on all sides, but a cuboid has varying length, breadth, and height.
Although both shapes appear to be almost identical, they have distinct qualities.
In this post, we will go into the definition, properties, and examples of Cubes and Cuboids. To learn more, keep reading.
Cuboid
A closed three-dimensional structure is encircled by rectangular faces, which are rectangle plane sections, in the cuboid shape. It has three dimensions: length, breadth, and height, and is one of the most common shapes in our world.
Faces, Vertices and Edges of Cuboid
Faces: A cuboid has basically 6 Faces
Vertices: A cuboid has 8 Vertices
Edges: A cuboid has 12 Edges
Properties of a Cuboid
Faces of a Cuboid
A cuboid is made up of six rectangles, each of which is referred to as a face. ABCD, DEFC, BCFG, ABGH, HEFG, ADEH are the six faces of a cuboid in the diagram above. A cuboid has two opposed faces with equal lengths and areas.
ABCD and HGFE, for example, are two opposing faces. The faces of a cuboid are all rectangular.
Edges of a Cuboid
In a cuboid, there are a total of 12 edges. AB, BC, CD, AD, DE, EF, FC, AH, HG, GB, HE, GF are the letters. The opposite edges of a cuboid are of equal length. AB=DC=HG=EF, AD=BC=HE=GF, and AH=BG=DE=CF, for example. In a cuboid, opposite edges are parallel to each other.
Vertices of a Cuboid
There are eight vertices in a cuboid. A, B, C, D, E, F, G, and H are the letters. The angles formed at the vertices of a cuboid are all right angles.
Face Diagonal
Connecting the opposite vertices on a cuboid’s face creates face diagonals. For example, in the Face ABCD, AC is a face diagonal. A cuboid can have a total of 12 face diagonals.
Space Diagonal
A space diagonal is a line segment connecting the opposite vertices of a cuboid. The interior of the cuboid has space diagonals running through it. As a result, it can be divided into four space diagonals. A space diagonal, for example, is HC.
How to identify a Cuboid
Each face of a cuboid is a rectangle, with 90-degree angles at the corners or vertices. Furthermore, the opposite faces are always the same. A book, for example, is a cuboid. It has six surfaces, each of which has the same dimensions as the opposing pair.
Total-Surface Area of Cuboid
If l is the cuboid’s length, b is its width, and h is its height, the sum of the areas of its six rectangles equals the cuboid’s total surface area. The formula is provided below.
Total Surface area of a Cuboid=2[l×b+l×h+b×h]
Lateral Surface Area of Cuboid
The lateral surface area of a cuboid is equal to the total of the areas of its four side faces, except the bottom and top faces. The sum of the area of a room’s four walls is an example of lateral surface area. The formula for calculating a cuboid’s lateral surface area is
Area of Four sides=2l×h + 2b×h=2(l+b)×h=Perimeter of Base×Height
Lateral Surface area of a Cuboid=2l×bh
Volume of Cuboid
A cuboid’s volume is calculated by multiplying its base area by its height. Therefore,
l× b× h = volume V= A× h To put it plainly,
V = l×b× h = volume of cuboid
Where l is the cuboid’s length, b is its base, and h is its height.
Diagonal of a Cuboid
The length of a cuboid’s longest diagonal is determined by
(l2 + b2 + h2) is the length of the cuboid diagonal.
Examples
In our daily lives, we see tall buildings, books, crates, mobile phones, televisions, microwaves, photo frames, mattresses, bricks, and other cuboids.
Cube
A cube is a three-dimensional object made up of six similar squares bound together in a closed shape. There are 6 faces, 12 edges, and 8 vertices in a cube. In other terms, a cube is a cuboid with the same length, width, and height.
Volume of Cube
The volume is calculated using the formula length (l) breadth (b) height (h). So because sides of a cube measure the same, a can be used to symbolise them. As a result, l = b = h = a. Therefore,
The volume of a cube is equal to l x b x h = a x a x a. alternatively,
Volume of Cube=a3
Where a is the length of each of the cube’s sides.
Differences between Cube and Cuboid
Conclusion
The cube and the cuboid are three-dimensional figures with six faces, eight vertices, and twelve edges. In a Cube, length, breadth, and height are all equal, but they are not in a Cuboid. The shapes, figures, example nets, and formulas of the Cube and Cuboid were examined in depth in this article.
The distinction between the Cube and the Cuboid aids in the comparison and understanding of the two. This article explains how to use appropriate formulas to solve problems with the Cube and Cuboid.
