A cube is a three-dimensional object that has 6 congruent square faces. Dimensions of all the 6 square faces of the cube are the same. A cube is sometimes also referred to as a regular hexahedron or as a square prism. It is one of the 5 platonic solids.
Some real-life examples of a cube are an ice cube, a Rubik's cube, a regular dice, etc. Let us learn about a cube along with its formulas, a few solved examples, and practice questions here.
|1.||What Is a Cube?|
|2.||What Is the Area of a Cube Formula?|
|3.||What Is the Volume of a Cube Formula?|
|4.||FAQs on a Cube|
What Is a Cube?
A cube is a 3-D solid object with six square faces and all the sides of a cube are of the same length.
The cube is also known as a regular hexahedron and is one of the five platonic solids.
What Is the Area of a Cube Formula?
There are two types of area of a cube
- Lateral area
- Total surface area
Lateral Area of a Cube
The lateral area of a cube is the sum of areas of all side faces of the cube. There are 4 side faces so the sum of areas of all 4 side faces of a cube is its lateral area.
The lateral area of a cube is also known as its lateral surface area (LSA), and it is measured in square units.
LSA = 4a2
where "a" is the side length.
Total Surface Area of a Cube
The total surface area of the cube will be the sum of the area of the base and the area of vertical surfaces of the cube. Since all the faces of the cube are made up of squares of the same dimensions then the total surface area of the cube will be the surface area of one face added five times to itself. It is measured as the "number of square units" (square centimeters, square inches, square feet, etc.)
What Is the Volume of a Cube Formula?
The volume of a cube is the space occupied by the cube. The volume of a cube can be found out by finding the cube of the side length of the cube.
The volume of a cube of side length "a" is a × a × a or a3 and it is expressed in cubic units of length.
What is the amount of water is stored in one ice-cube of side length 5 in?
Length of the ice-cube = 5 inches
Amount of water stored in the ice-cube = Volume of the cube
Therefore, the volume of the ice-cube = 5 × 5 × 5 in3
= 125 in3
Answer: The amount of water in the ice is 125 in3.
Find the total surface area of the cube if the length of the side of the cube is 25 in.
Length of the side of the cube, a = 25 in
Using the formula for the area of the cube, which is: A = 6a2
A = 6 × 25 × 25
A = 3750
Answer: The surface area of the cube is 3750 square inches.
FAQs on Cube
Why Is a cube Called a Regular Hexahedron?
A regular hexahedron is a three-dimensional object with 6 congruent faces. Thus, a cube is called a regular hexahedron.
What Is the Formula For the Lateral Area of a Cube?
The lateral area of a cube of edge length 'x' is 4x2 square units.
How Do You Find the Lateral Area of a Cube?
The lateral area of a cube of edge length 'x' can be obtained by adding the areas of 4 side faces. Thus, the lateral area of the cube = x2 + x2 + x2 + x2 = 4x2.
What Is the Difference Between the Surface Area and Lateral Area of a Cube?
The surface area (or) total surface area (TSA) of a cube is the sum of areas of all faces whereas the lateral surface area (LSA) is only the sum of the 4 side faces of the cube. If x is the edge length of the cube, then
- Total Surface Area (TSA) = 6x2
- Lateral Surface Area (LSA) = 4x2
What Is Surface Area and Area?
Usually, the term "area" is used to represent the space enclosed by a two-dimensional object. The "surface area" is used to represent the sum of the areas of all faces of a three-dimensional object.
What Is the Volume of a Cube?
The volume of a cube is a3, where a is the length of the side of the cube.
What Is the Formula to Find the Area of the Base of a Cube?
The formula to find the area of the base of a cube is a2, where a is the length of the side of the cube.
What Do the 5 Platonic Solids Represent?
The cube represents the earth, the octahedron represents the air, the tetrahedron represents the fire, the icosahedron represents the water, and the dodecahedron represents the universe.