Formula of Surface Area of a Cube
What is a cube?
A cube is a 3-D solid shape, which has a total of 6 sides.
A cube is one of the simplest shapes in three-dimensional space.
Sometimes, the shape cube is considered as “cubic”.
We can also say that a cube is considered as a block, where all the length, breadth, and height are the same.
Along with that, a cube has 8 vertices and 12 edges such that 3 edges meet at one vertex point.
Surface Area of Cube Definition
The definition of the surface area of a cube states that the total surface area is equal to the sum of all the areas of the faces of the cube. Since the cube has six faces, therefore, the total surface area of the cube will be equal to the sum of all six faces of the cube.
Since the surface of the cube is in the shape of a square. Hence, the area of each face of the cube can be said to be equal to the square of the edge. Let the length of the edge of a cube be a.
Area of one face = a2
There are a total of 6 faces. Therefore,
Total Surface Area of cube Formula = a2 + a2 + a2 + a2 + a2 + a2
Total Surface Area of cube Formula = 6a2
A cube consists of an ‘n’ number of square units. Hence the surface area is the space covered by these square units on the surface of the cube. Basically, the surface area is the sum of all the areas of all the shapes that cover the surface of the shape. In the case of a cube, the number of faces is 6. So the surface area will be the sum of all the areas of six faces.
Now, let us derive the formula for surface area for a given cube, to solve problems based on it.
Surface Area of a Cube Formula
As per the definition of the cube we have discussed above, we know, the cube consists of 6 square faces. Let us consider a cube whose length of the edges is denoted by the letter ‘a’.
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We know, by the formula of area of a square = side2 = a2
Therefore, the total surface area of cube formula = 6 × (area of each side)
= 6 × a2 = 6a2 Square Unit.
Solved Examples
What is the surface area of a cube of side equal to 5 cm?
Solution: Given,
Side of the cube equals a = 5 cm
Total Surface Area of Cube formula = 6a2
= 6 × 5 × 5
= 6 × 25 cm2
= 150 cm2
What is the surface area of a cube of side equal to 17 cm?
Solution: Given,
Side of the cube equals a = 17 cm
Total Surface Area of Cube formula = 6a2
= 6 × 172cm2
= 6 × 289 cm2
= 1734 cm2
Calculate the cost of painting an aquarium that is in the shape of a cube with a 10m edge length. If the cost of painting an aquarium is INR 3/m*2, how much does it cost to paint an aquarium?
Solution: The aquarium's total surface area is 6 square feet (side)^ 2
=6102
= 600 square meters
The total cost of painting the aquarium = 3 × 600 = Rs. 1800
Find the overall surface area of a cubic construction if the sidewalls are 7 meters long.
Solution: Assume the sidewall is 7 meters long.
We know what the formula says;
TSA = 6a2
6 x 7 x 7 = 294 sq.m = TSA
Conclusion
This is how the surface area of a cube is calculated. Learn how the formula is derived following the features of a cube and then utilized to calculate its surface area. Focus on how this formula is used in the solved examples to grab hold of the concept well.
FAQs on Surface Area of a Cube Formula
1. How do you calculate a cube's surface area?
To find the surface area of a cube, multiply the size of one of the square sides by 6, because there are six sides. This is equivalent to solving with the formula Total surface Area of Cube = 6s2.
2. What is the Surface Area Formula?
Surface area can be defined as the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. Taking the length as (l), width as (w), and height as (h) of the prism and the formula, SA = 2lw + 2lh + 2hw, to find the surface area.
3. What is the distinction between a cube and a cuboid?
The main distinction between a cube and a cuboid is that a cube has six identical square-shaped faces, whereas a cuboid has rectangular faces. Although the structure of a cube and a cuboid are similar, they have a few differences in terms of edge length, diagonals, and faces.
4. What is a Cube?
A cube is a three-dimensional object with six square faces that are all the same size. All six square faces of the cube have the same dimensions. A regular hexahedron or a square prism are two other names for a cube. A cube can be anything from an ice cube to a Rubik's cube to a conventional dice. There are six square faces, eight vertices, and twelve edges in this puzzle. make up a cube.
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