One may determine a cube’s surface area, diagonals, and volume using the Cube Formula. The volume of a cube with an edge length equal to a particular number is directly represented by its cube. A cube is a solid, three-dimensional object having six square faces and equal-length sides. Finally, students can learn about the Cube Formula by working through a few examples cited on the Extramarks website and mobile application.
A cube is a solid, three-dimensional object with six square faces. With six equal faces, eight vertices, and twelve equal edges, it is a geometric shape. Examples of cubes in real life include Rubik’s cubes, dice, and ice cubes, among others. Students may determine a cube’s surface area, diagonals, and volume using the Cube Formula.
Introduction – What is a Cube?
A number raised to the power 3 is referred to as a cube in algebra. The word “cube” has a different meaning in geometry, where it refers to a three-dimensional object with equal numbers of faces and edges.
Given that the cube has equal length, breadth, and height, we can also calculate the volume of the Cube Formula based on this.
Height = a * Length * Breadth
Therefore, each cube’s edge’s measurement is equal to a.
The volume of the Cube Formula is therefore a a a = a3.
The number derived using the Cube Formula is the ideal cube number, it should be emphasised.
The main distinction between the square and the cube is that the square is a two-dimensional figure with just length and width, whereas the cube is a three-dimensional form with length, breadth, and height as its three dimensions. The square shape is used to create the cube.
A three-dimensional object with six congruent square faces is called a cube. The cube’s six square faces all have the same dimensions. A square prism or a regular hexahedron are two other names for a cube. One of the five platonic solids, it. An ice cube, a Rubik’s cube, a standard dice, etc. are a few instances of cubes in everyday life.
Properties of Cube
A cube is a solid, three-dimensional shape with six square faces, eight vertices, and twelve edges that is used in mathematics or geometry. Also said to be a conventional hexahedron. The three-by-three Rubik’s cube, which is the most prevalent example in real life and is useful for boosting brain function, must have been seen by the students. Students will also encounter several real-world instances, such as six-sided dice, etc. Three-dimensional structures and figures with surface areas and volumes are the focus of solid geometry. The cuboid, cylinder, cone, and sphere are the other solid shapes. Here, students will talk about Cube Formula meaning, characteristics, and relevance to mathematics. Students will also learn the Cube Formula as well as its surface area formula.
The following are the important 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 angles.
- 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.
What is the Cube Formula?
The Cube Formula are addressed below:
Cube Surface Area
Students must be aware that the region a shape occupies in a plane is what is meant by the term “area” for every shape. Because a cube is a three-dimensional object, the space it takes up will be in a three-dimensional plane. Because a cube has six faces, they must calculate the surface area of the cube covered by each face.The formula for calculating surface area is provided below.
Let a serve as the cube’s edge.
Square root of the area of a face is equal to a2.
The cube is known to have six square-shaped faces.
The area of one face divided by four equals the lateral surface area (top and bottom faces excluded).
LSA = 4a2
LSA + Area of the Top and Bottom Faces = Total Surface Area
TSA = 4a2 plus a2 plus a2
TSA = 6a2
Surface Area of Cube = 6a2 in a square units
Surface Area of a Cube Formula
The amount of room a cube can hold is measured by its volume. If an object has a cubic shape and we need to fill it with anything, let’s say water, then the amount of water in litres that needs to be kept inside the object is determined by its volume. The volume formula is provided by:
Cube volume equals a3 cubic units.
Examples Using Cube Formula
Determine the cube’s surface area and volume if the side length is 10 cm.
Solution: If side a = 10 cm, then
Consequently, using the cube’s surface area and volume equations, we may write;
Surface Area = 6a2 = 6102 = 6100, which is 600 cm2.
A3 = 103 = 1000 cm3 is the volume.
Discover the cube’s side length. Its volume is 512 cm3.
Solution: Given, Cube’s volume, v = 512 cm2.
We are aware that a3 cubic units is the formula for a cube’s volume.
512 thus equals a3
You can represent 512 as 83.
83 = a3
Consequently, a= 8
As a result, the cube’s side length is 8 cm.
FAQs (Frequently Asked Questions)
1. Describe a cube.
Having six faces, eight vertices, and twelve edges, a cube is a three-dimensional figure. A prism is simply a specific instance of a cube.
2. What distinguishes a cube from a cuboid?
All of a cube’s faces are square, making it a three-dimensional version of the square. The faces of a cuboid, on the other hand, are all rectangles in three dimensions.
3. Note the equation for calculating a cube's surface area.
The formula to get a cube’s surface area is 6a2 square units, where “a” stands for the cube’s side length.
4. How do you determine a cube's volume using the Cube Formula?
The volume of a cube is calculated as a3 cubic units, where “a” is the side length, because every side of a cube is equal.