In Geometry, we have studied different two-dimensional and three-dimensional figures, like the square, rectangle, circle, cube, cuboid, sphere, and many more. When we look at cube and cuboid at a glance they appear to be the same figure, but some of their properties distinguish them from each other. So let us study what is cube and cuboid, different properties of cube and cuboid, and see what is the difference between cube and cuboid?
A cube is a three-dimensional figure composed of square-shaped faces of the same size. All the angles of a cube meet at 900. A cube has 6 equal faces, and all the faces are square-shaped. It has 8 vertices and 12 equal edges.
The below figure represents a cube, where l is length, b is the breadth, and h is height and l = b = h. The length, breadth, and height represent the edges of the cube. And when the three edges meet at a point it is called a vertex.
Properties of Cube
A cube has all its faces as a square-shaped.
All the faces and edges are equal.
The angles of the cube are at right angles.
Each of the faces meets the other adjacent four faces.
Each of the vertices meets the three faces and three edges.
The edges opposite to each other are parallel and also equal.
A cuboid is a three-dimensional figure composed of rectangular faces. A cuboid is a box-shaped figure. A cuboid also has 12 edges and 8 vertices. The faces and edges of the cuboid are not equal. On the contrary the opposite faces of the cuboid are equal.
The below figure represents the cuboid. Where l is the length, b is the breadth, and h is the height, l \[\neq\] b \[\neq\] h.
Any face can be the bottom face of the cuboid and the remaining four adjacent faces are called the lateral faces of the cuboid.
Properties of Cuboid
A cuboid consists of six rectangular faces.
Opposite faces of the cuboid are equal.
Opposite edges of a cuboid are equal.
The intersection of three faces is a vertex of a cuboid.
The angles of the cuboid are at right angles.
As we now know what is cube? What is a cuboid? Let us study cube and cuboid difference i.e cube vs cuboid.
Though cube and cuboid are three-dimensional figures with 12 faces, 12 edges, and 8 vertices, they are different from each other. So let us study what is the difference between cube and cuboid? The properties which distinguish them from each other as follows:
S.No | Cube | Cuboid |
1 | All the edges(sides) of a cube are equal i.e the measures of length, breadth, and height are equal. | All the edges(sides) of a cuboid are not equal i.e the measures of length, breadth, and height are not equal. |
2 | Cube is a 3-dimensional shape of a square | The cuboid is a 3-dimensional shape of a rectangle |
3 | All the six faces of a cube are square shapes. | All the six faces of a cuboid are rectangles |
4 | All the 12 diagonals on the surface are of the same measure | It has 12 diagonals. But in the set of 4 diagonals, 3 diagonals are of different measures |
5 | All the 4 internal diagonals are equal | It has 4 internal diagonals. But the two pairs are of different measures |
6 | Examples of the cube are Ice cube, Dice, Rubik’s Cube | Examples of cuboids are Bricks, Duster. |
7 | Lateral Surface Area = 4 × (edge)2 | Lateral Surface Area= 2 (l + b) h where, l = length, b = breadth and h = height |
8 | Total Surface Area = 6 × (edge)2 | Total Surface Area = 2 (lb + bh + hl)where,l = length, b = breadth and h = height |
9 | Diagonal = √3 × (edge) | Diagonal = \[\sqrt{l^{2}+b^{2}+h^{2}}\] where, l = length, b = breadth and h = height |
10 | Volume = (edge)3 | Volume = l × b × h where,l = length, b = breadth and h = height |
11 | Perimeter = 12 (edge) | Perimeter = 4(l + b+ h) where, l = length, b = breadth and h = height |
These will make the concept of cube vs cuboid crystal clear.
Example 1: Find the total surface area of the cuboid with dimensions length = 4 cm, breadth = 3cm, and height = 7 cm.
Solution:
We have,
Total Surface Area od cuboid = 2 (lb + bh + hl )
= 2 ( 4×3 + 3×7 + 7×4)
= 2 ( 12 + 21 + 28 )
= 2 x 61
= 122 cm2
So, the total surface area of this cuboid is 122cm2.
Example 2: Find the surface area of a cube having its sides equal to 5 cm in length.
Solution: Given length = edge = 5 cm
We have, Surface area of cube = 6 ( edge)2
= 6× 52
= 6 × 25
= 150 cm2
The length, width, and height of a cuboid are 10 cm, 12 cm, and 14 cm respectively. Find the lateral surface area and total surface area of a cuboid.
If the value of the side of the cube is 9cm, then find surface area and volume of the cube.
1. Is Cube A Square?
The basic differences between cube and square is of dimensions. A square is a two-dimensional figure with two dimensions length and breadth, while a cube is a three-dimensional figure with three dimensions length, breadth, and height.
The side faces of a cube are formed by squares. The square has four sides and four vertices, whereas the cube has 12 edges(sides) and 8 vertices.
From this properties we can say the cube is a 3-dimensional figure formed by the square-shaped faces.
2. What Is A Cube Formula?
A cube is a three-dimensional object, therefore space occupied by the cube will be 3D.
A cube is bounded by six square faces so the surface area will be calculated by adding the area of all the six square faces. Therefore the surface area of the cube is
Surface Area of Cube = 6(side)^{2} |
And the volume of the cube is the space occupied by it. The Volume of the cube will be calculated as
Volume = (side)^{3} |
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