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**Surface Area of a Cube Formula**

**Introduction:**

Surface area refers to the total measure of the outer or exposed area of a three-dimensional object. It represents the sum of all the areas of the individual faces or surfaces of the object. Surface area is commonly calculated for various geometric shapes such as cubes, rectangular prisms, cylinders, spheres, and more. The calculation of surface area allows for the determination of the amount of material needed to cover or enclose an object, among other practical considerations.

**What is meant by Surface Area of a Cube?**

The surface area of a cube is the measure of the total area covered by all six faces of the cube. Each face of a cube is square with equal side lengths. To find the surface area of a cube, we use the formula SA = 6s2, where SA represents the surface area and s represents the length of the side of the cube. The surface area of a cube is essential for various geometric calculations and real-world applications, such as packaging design and material estimation.

**How to find the surface area of a cube?**

A cube is made up of square faces. Hence, its length, breadth, and height are equal.

The surface area of a cube is the sum of the areas of its 6 square faces.

For a cube with length, breadth and height as s units, the area of each face will be s2 units.

**Total surface area of a cube:** The total surface area of a cube is the sum of the areas of all its faces, including the top, bottom, and lateral faces. Since a cube has six congruent square faces, the total surface area can be calculated by multiplying the area of one face by six.

∴ Total surface area of cube (TSA)= 6s2

**Lateral surface area of a cube:**

The lateral surface area of a cube refers to the combined area of all its faces excluding the top and bottom faces. Since a cube has six congruent square faces, the lateral surface area can be calculated by multiplying the length of one side of the cube by itself and then multiplying that by four.

Therefore, the lateral surface area of the cube includes the 4 squares at the side.

It is given by 4s2.

**Solved Examples on Surface Area of Cube:**

**Example 1**: A cube-shaped gift box has a side length of 10 centimeters. What is the total surface area of the gift box?

Solution:

The formula for the total surface area (TSA) of a cube is TSA = 6s2.

Given that the side length of the cube is 10 centimeters, we can calculate the total surface area as follows:

TSA = 6s2

TSA = 6 x 100

TSA = 600 square centimeters

Therefore, the total surface area of the gift box is 600 square centimeters.

**Example 2:** A cube has a total surface area of 216 square meters. What is the length of each side of the cube?

Solution:

We need to find the side length of the cube when given its total surface area.

The formula for the total surface area (TSA) of a cube is TSA = 6s2

Given that the total surface area of the cube is 216 square meters, we can set up the equation as follows:

216 = 6s2

To isolate the side length, we divide both sides of the equation by 6:

216 / 6 = s2

36 = s2

Now, we take the square root of both sides to solve for the side length.

√36 = √s2

6 = side length

Therefore, the length of each side of the cube is 6 meters.

**Frequently Asked Questions on Surface Area of Cube:**

1: What is the surface area of a cube?

Answer: The surface area of a cube is determined by finding the sum of the areas of all its six square faces. Since all the faces of a cube are congruent, the surface area formula for a cube is given by 6 times the square of the length of one of its edges. In other words, the surface area of a cube can be calculated as 6 times the side length squared.

2: What is the formula for finding the total surface area of a cube?

Answer: The formula for the surface area of a cube is TSA = 6s2. It involves multiplying the square of the side length by six since a cube has six congruent square faces. This formula allows for a straightforward calculation of the total surface area of a cube.

3: What is the surface area of a box?

Answer: The surface area of a box, also known as a rectangular prism, is the sum of the areas of all its six faces. To calculate the surface area, you need to find the area of each face (top, bottom, front, back, left, and right) and add them together. The formula for the surface area of a box is 2 times the sum of the products of the length and width of each pair of adjacent faces, plus 2 times the sum of the products of the width and height, and the length and height.

4: What is the Curved Surface Area of Cube Formula?

Answer: The curved surface area (CSA) of a cube refers to the combined area of all the lateral or side faces of the cube. It is often abbreviated as CSA. The formula used to calculate the curved surface area of a cube is CSA = 4s2, where ‘a’ represents the edge length of the cube.

5: What is the surface area of cuboid?

Answer: The surface area of a cuboid is the sum of the areas of all its six rectangular faces. To calculate the surface area, you need to find the area of each face (top, bottom, front, back, left, and right) and add them together. The formula for the surface area of a cuboid is 2 times the sum of the products of the length, width, and height of each pair of adjacent faces.

6: How many faces does a cube have?

Answer: A cube has six faces. All of these faces are congruent squares, meaning they have equal side lengths and angles. The six faces of a cube are arranged in a way that forms a regular hexahedron, making it one of the simplest and most symmetrical three-dimensional shapes.

7: Is CSA and LSA same for a cube?

Answer: Yes, for a cube, the CSA (Curved Surface Area) and LSA (Lateral Surface Area) are the same. Since a cube does not have curved surfaces, the lateral surface area, which represents the area covered by the side faces of the cube, is equivalent to the curved surface area. Therefore, in the case of a cube, CSA and LSA can be used interchangeably to refer to the surface area of the side faces of the cube.

8: How to Find the Surface Area of Cube When Volume is Given?

Answer: To find the surface area of a cube when the volume is given, follow these steps:

- Begin with the formula for the volume of a cube: V = (side length)3.
- Rearrange the formula to solve for the side length: side length = cube root of (V).
- Take the cube root of the given volume to determine the length of each side.
- Once you have the side length, use the formula for the surface area of a cube: TSA = 6 x (side length)2.
- Substitute the value of the side length into the formula and calculate the surface area.

By using the given volume to find the side length and then applying the surface area formula, you can determine the surface area of the cube.