No, the lateral surface area of a cube cannot be negative. Surface area is always a positive quantity because it represents the area of the surfaces, which is inherently positive. If a calculation results in a negative value, it indicates an error in measurement or calculation.
About Lateral Surface Area of a Cube
A cube's lateral surface area is equal to the total area of the cube's side faces. A cube is a three-dimensional object with six congruent square faces. The cube's six square faces are all the same size. A cube is also known as:
A normal hexahedron (since it has six congruent faces) and a square prism (as its top and bottom faces are squares)
A cube is 1 of the five platonic solids to be noticed. A Rubik's cube, a dice (with square faces), an ice cube, and other real-life cubes are examples. Let's look at what the lateral surface area of a cube is, as well as the formula, a few examples, and some practice questions.
The formula for Lateral Surface Area (L.S.A) of a Cube
'Lateral' refers to something that is on the side. As a result, a cube's lateral surface area is equal to the sum of its side faces. Can you figure out how many sides a cube has? Yes, there are four sides (because there are 6 faces in total, among which if we remove the top and the bottom faces, there are only 4 side faces). The lateral area of a cube is equal to sum of its four side faces. A cube's lateral area is also known as its lateral surface area (LSA). The area of the lateral surface is measured in square units.
Consider a cube of edge length 'x'. Each of its faces is a square, the area of each face = x2 square units.
The lateral surface area (LSA) of cube = sum of areas of all four side faces ⇒ LSA of the cube = x2 + x2 + x2 + x2 = 4x2
L.S.A = 4x2
Lateral Surface Area (L.S.A) of Cube with Diagonal
We need to remember the link between the edge length (x) and the space diagonal (d) of a cube in order to compute the lateral area of a cube when the space diagonal is given. The relationship between a cube's side length (x) and its space diagonal (d) is given by
d = x √3 ⇒ x = d / √3
Substituting this in the formula of the lateral surface area of a cube,
L.S.A = 4x2
= 4 (d / √3)2
= 4d2 / 3
Thus, the LSA of the cube when its diagonal (d) is given = 4d2 / 3. The lateral area of a cube of the edge length 'x' is 4x2 & the lateral area of a cube of space diagonal 'd' is 4d2/ 3.
Download free pdf of Lateral Surface Area of a Cube Its Use And Solved Examples
Frequently Asked Questions
The lateral surface area of a cube refers to the total area of the four vertical faces (excluding the top and bottom faces). It is calculated by multiplying the perimeter of one face by the height of the cube. In a cube, all the faces are square-shaped, so the lateral surface area is simply the area of the four sides.
To calculate the lateral surface area of a cube, use the formula:
Lateral Surface Area = 4 × (side length)²
Where "side length" is the length of any edge of the cube. This formula accounts for the four side faces of the cube.
The total surface area of a cube includes the area of all six faces (top, bottom, and the four sides), while the lateral surface area only includes the area of the four vertical sides, excluding the top and bottom faces.
The formula for total surface area is:
Total Surface Area = 6 × (side length)²
To calculate the lateral surface area, use the formula:
Lateral Surface Area = 4 × (side length)²
Substitute the side length (5 cm):
Lateral Surface Area = 4 × (5)² = 4 × 25 = 100 cm²
So, the lateral surface area is 100 cm².
The lateral surface area of a cube is important in various real-life scenarios such as packaging, material coating, and construction. For example, when wrapping a cube-shaped object with paper, you would only need to consider the lateral surface area (the sides) if you exclude the top and bottom. It's also useful for calculating the amount of paint required to cover the sides of a cube-shaped box.