Show
The surface area of a 3D shape (solid object) is a measure of the total area that the surface of the object occupies. The surface area of a cube is the total area covered by all six faces of the cube. The total surface area of a cube can be calculated if we calculate the area of the two bases and the area of the four lateral (side) faces. It’s important to know and understand the surface area as it helps you to know the amount of sheet of paper required to wrap a cube, paint the surfaces of the cube, etc. Let’s learn how to find the surface area of a cube and its uses. Cube – A 3D Solid ShapeA cube(or regular hexahedron) is a 3D solid shape with six square faces and all the edges (or sides) of a cube are of the same length. The shape consists of six square faces, eight vertices, and twelve edges. The length, width(or breadth), and height are of the same measurement in a cube since the 3D figure is a square that has all sides of the same length.  A cube has the following properties:
Difference Between Cube and CuboidAlthough cube and cuboid are similar $3D$ objects, there are few differences between these two. Following are the differences between a cube and a cuboid.
Maths can be really interesting for kids What is the Surface Area of a Cube?The surface area of a cube is the sum of the area of the bases($2$ bases) and the area of lateral faces($4$ lateral faces) of the cube. Since all six faces of the cube are made up of squares of the same dimensions then the total surface area of the cube will be numerically equal to six times the area of one face. The surface area of a cube is measured as the “number of square units” ($cm^{2}$, $m^{2}$, $in^{2}$, $ft^{2}$, etc.). There are two types of surface areas of a cube
Lateral Surface Area of a CubeThe lateral surface area of a cube refers to the total area covered by the side or lateral faces of a cube. There are four lateral faces in a cube, so to calculate LSA, we find the sum of the areas of these $4$ square faces. If $a$ is the length of the edge (side) of a cube, then the area of one face (square) is $a \times a = a^{2}$ sq units. Therefore, the lateral surface area (LSA) of a cube is $4 \times a^{2} = 4a^{2}$ sq units. Formula for Lateral Surface Area = $4a^{2}$. Total Surface Area of a CubeThe total surface area of a cube refers to the total area covered by all the faces of a cube. There are six square faces in a cube, so to calculate TSA, we find the sum of the areas of these $6$ faces. If $a$ is the length of the edge (side) of a cube, then the area of one face (square) is $a \times a = a^{2}$ sq units. Therefore, the total surface area (TSA) of a cube is $6 \times a^{2} = 6a^{2}$ sq units. Formula for Total Surface Area = $6a^{2}$. ExamplesEx 1: Find the area of the metal sheet required to make a cubical box of side length $4 cm$. .Length of side of cubical box = $a = 4 cm$ Amount of metal sheet required to make a cubical box = Total Surface Area of a Cube = $6a^{2}$ $6a^{2} = 6 \times 4^{2} = 6 \times 16 = 96 cm^{2}$ Therefore, the area of the metal sheet required to make a cubical box of side length $4 cm$ is $96 cm^{2}$. Ex 2: Find the ratio of the lateral surface area and total surface area of a cube. Let the side of a cube be $a$ units Lateral surface area = $4a^{2}$ sq units Total surface area = $6a^{2}$ sq units The ratio of LSA to TSA is $4a^{2} : 6a^{2} = \frac {4a^{2}}{6a^{2}} = \frac {4}{6} = \frac {2}{3} = 2 : 3$. Ex 3: Find the length of the edge of the cube whose total surface area is $384 cm^{2}$. TSA of cube = $384 cm^{2}$ $6a^{2} = 384 => a^{2} = \frac {384}{6} => a^{2} = 64 => a = 8 cm$ Length of the edge of a cube = $8 cm$ Maths in Real Life ConclusionThe surface area of a 3D shape (solid object) is a measure of the total area that the surface of the object occupies. There are two types of surface areas in a cube, viz., lateral surface area calculated using the formula $4a^{2}$ and total surface area calculated using the formula $6a^{2}$, where $a$ is the length of each side of a cube. Practice Problems
Recommended Reading
FAQsHow to find the surface area of a cube?Each face of the cube is a $2D$ plane figure which is a square. The area of a square is equal to $a^{2}$, where $a$ is the length of the edge(or side) of a cube. Since there are six faces of a cube, therefore the total surface area or surface area of a cube will be equal to the sum of areas of all its faces, i.e. $6a^{2}. What is the formula for the surface area of a cube?There are two types of surface areas in a cube. What is the unit used to express the surface area of a cube?The surface area of a cube is expressed in square units, for example using units like $cm^{2}$, $m^{2}$, $ft^{2}$, $in^{2}$ etc. What is the total surface area of a cube?The total surface area is the region occupied by all six faces of the cube in a three-dimensional space. The formula used to find the total surface area is $6a^{2}$, where $a$ is the edge(or side) length of the cube. What is the lateral surface area of a cube?The lateral surface area of a cube refers to the total area covered by the side or lateral faces of a cube in a three-dimensional space. The formula used to find the total surface area is $4a^{2}$, where $a$ is the edge(or side) length of the cube. You May Also LikeTable of Contents What is a Bar Graph?Types of Bar GraphsVertical Bar
Table of Contents What is a Pictograph?How to Read a PictographExamplesHow to Table of Contents What is Data?What is Primary Data?What is Secondary Data?Difference
What is LSA and TSA of cube?The surface area of a cube with edge length as 'a' can be calculated using the following formulas, LSA of Cube = 4a2 square units and, TSA of Cube = 6a2 square units.
What is the lateral surface area of cube class 9?Lateral surface area of a cuboid is 2(l + b)h. III. Lateral surface area of a cube is 4a2.
|
Formula of lateral surface area of cube
Related Posts
Copyright © 2024 nguoilontuoi Inc.
