In Maths or in Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces or sides, 8 vertices and 12 edges. It is also said to be a regular hexahedron. You must have seen 3 × 3 Rubik’s cube, which is the most common example in the real-life and it is helpful to enhance brainpower. In the same way, you will come across many real-life examples, such as 6 sided dices, etc. We will discuss here its definition, properties and its importance in Maths. Also, learn the surface area formula for the cube along with its volume formula.
Solid geometry is all about three-dimensional shapes and figures, which have surface areas and volumes. The other solid shapes are;
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As discussed earlier, a cube is a 3-D solid shape, which has 6 sides. Along with that, it has 8 vertices and 12 edges such that 3 edges meet at one vertex point. Check the given image below, defining its faces, edges and vertices. It is also mentioned as a square parallelepiped, an equilateral cuboid and a right rhombohedron.
In the above figure, you can see, edge, face and vertex of the cube. Here, L stands for length, B stands for breadth and H stands for height. We can see, the length, breadth and height of the cube, which represents the edges of the cube, connects at a single point which is the vertex. The faces of the cube is connected by four vertices.
Surface Area and Volume Formula For Cube
We have discussed until now the definitions and properties of the cube along with its importance in solid geometry. Now let us learn its formula. The two major formulas are for surface area and volume of a solid shape.
Surface area of Cube
Since, for any shape, the area is the region occupied by it in a plane. A cube is a three-dimensional object, therefore, the area occupied by it will be in 3d plane. Since a cube has six faces, therefore, we need to calculate the surface area of the cube, covered by each face. Hence, the formula for surface area is given by:
Volume of Cube
The volume of the cube is the space contained in it. Suppose, if an object is in cubical shape and we need to immerse any material in it, say water, then the measure of waters in litres to be kept in the object is calculated by its volume. The formula of the volume is given by:
Length of Diagonal of Side
If a is the length of the side, then,
- Length of Diagonal of Face of the Cube = √2 a
- Length of Diagonal of Cube = √3 a
Properties of Cube
- It has all its faces in a square shape.
- All the faces or sides have equal dimensions.
- The plane angles of the cube are the right angle.
- Each of the faces meets the other four faces.
- Each of the vertices meets the three faces and three edges.
- The edges opposite to each other are parallel.
1. If the value of the side of the cube is 10cm, then find its surface area and volume.
Given, side , a = 10cm
Therefore, by the surface area and volume formula of the cube, we can write;
Surface Area = 6a2 = 6 × 102 = 6 × 100.= 600 cm2
Volume = a3 = 103 = 1000 cm3
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