What is Cube in Maths?
We are surrounded by different things that are made of different geometrical shapes. Consider a children’s block game or a playing dice or an ice cube. What do you observe common among this all? They all have the shape of a cube, isn’t it? In this article, we will study what is a cube? The volume of cube formula, area of cube formula, the surface area of a cube formula. Some of the common examples of the cube are Ice cube, Dice, Rubik’s Cube
What is Cube?
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.
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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.
All the 12 diagonals on the surface are of the same measure
All the 4 internal diagonals are equal
Surface Area of a Cube Formula
The surface area is the area calculated for the three- dimensional object. As the three-dimensional object is made up of 2D faces, the surface area is the sum of the areas of all the faces of the figure. Therefore to find the surface area of 3D objects we have to add the area of all its faces. We can use the basic area formula to calculate its faces as they are simple 2D figures,
For example, a cube has six faces. Therefore, its surface area will be the sum of the areas of all the six faces. Since all the sides of a cube are squares, we can express the surface area of a cube as 6 x (Area of a square)
Basically, the surface area can be classified as:
Curved Surface Area (CSA).
The curved surface area of an object is the area of all the curved surfaces in an object.
Lateral Surface Area (LSA)
The lateral surface of an object is the area of all the faces of the object, excluding the area of its base and top. For a cube, the lateral surface area would be the sum of area of four sides i.e 4 x side.
Total Surface Area (TSA)
Total surface area is the area of all the faces including the bases.
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 cube formula is
The Volume of Cube Formula
The space occupied by the three-dimensional object is measured in terms of the volume of that object. The volume of a solid shape is the product of three dimensions, so the volume is expressed in cubic units. Suppose the volume of a cube is measured by the product of its length, width, and height.
The interior of a hollow object can be filled with air or some liquid that takes the shape of the object. In such cases, the volume of the substance that the interior of the object can accommodate is called the capacity of the hollow object. Thus we may say that the volume of an object is the measure of the space it occupies and the capacity of an object is the volume of the substance its interior can accommodate.
And the volume of the cube is the space occupied by it. The Volume of the cube formula will be calculated as
Solved Examples
Example 1: Find the surface area of a cube having its sides equal to 7 cm in length.
Solution:
Given length = edge = 7 cm
We have, Surface area of cube = 6 ( edge)2
= 6× 72
= 6 × 49
= 294 cm2
Example 2: The side of the cubic box is 9m. Find the volume of a cubic box.
Solution:
Given, Side = a = 9m
By the formula of volume of a cube, we know that
V = a3
V = 9 x 9 x 9
V = 729 sq.m or 729m2
Quiz Time
What is the volume of a cube of side 11.5 cm?
If the volume of a cube is 343 cm3, then what is the measure of the edge of a cube?
1. What is Cuboid?
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 ≠ b ≠ h.
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Any face can be the bottom face of the cuboid and the remaining four adjacent faces are called the lateral faces of the cuboid.
2. Differentiate Between Cube and Cuboid
Cube Vs Cuboid
Sr.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 = √(l² + b² + h²) 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 |