Lateral Area Formula
Lateral Area Formula
Any solid object’s lateral area may be calculated using the Lateral Area Formula. Any figure’s lateral area only includes the non-base faces. Calculating the lateral surface area of various figures, such as a cuboid, cube, cylinder, cone, or sphere, is made easier with the aid of the Lateral Area Formula. On the Extramarks website and mobile application, students can find more information about the Lateral Area Formula as well as a few examples that have been solved.
Distinct sorts of objects have a different Lateral Area Formula. As a result, there exist several Lateral Area Formula that are described on the Extramarks website and mobile application. The object’s base and the face parallel to the base are not included in the Lateral Area Formula.
What Is the Lateral Area Formula?
The Lateral Area Formula of an item is its whole, except its base and top (when they exist). Laminar surface zone equals Lateral Area Formula. This is to be contrasted with the total surface area, which includes the lateral surface area combined with the areas of the base and top regions.
List of Lateral Area Formula
- Lateral Area of Cube:
A cube has six faces of equal size and twelve edges of equal length. This is its lateral surface area. As a result, the cube’s lateral surface area is equal to 4 * side2.
L.S.A = 4 (a)2
- Lateral Area of Cuboid:
A three-dimensional shape called a cuboid has rectangles for all of its sides. It contains six rectangular faces, eight vertices, and twelve edges. Right angles are formed by the rectangular faces. As a result, the following formula for the cuboid’s lateral surface area is provided:
LSA equals 2(l + b)h
Where l denotes the length of a cuboid, b denotes its width, and h denotes its height.
- Cylinder Lateral Surface Size:
The area of the rectangle that encircles the cylinder’s side is known as the lateral surface area. As a result, the following formula for the cylinder’s surface area is provided:
L.S.A = 2 * π * r * h
Where pie = 22/7 or 3.14, r is a cylinder’s radius and h is the cylinder’s height.
- Cone’s Lateral Surface Area:
The cone’s lateral surface area consists only of the side or lateral surfaces. The cone’s lateral surface area may be computed as follows:
L.S.A = π * r * l
Where l is the slant height, r is the radius, and pie = 22/7 or 3.14. The shortest distance along the surface of the solid from the base to the apex is known as the slant height.
- The sphere’s lateral surface area is:
The sphere’s lateral surface area and a cylinder’s lateral surface area are connected.
L.S.A. of the cylinder = 2*r*h
where h = 2r.
Thus, the sphere’s lateral surface area is equal to 4 * r2.
- The areas of a pyramid’s lateral faces are added together to form the pyramid’s lateral surface area.
L.S.A = 1/2 pl
where l is the height of the slant and p is the base’s perimeter.
The formulas for calculating the Lateral Area Formula have been mentioned above with explanations. The lateral surface area of a figure is the total surface area excluding the top and bottom of the figure.
Examples on Lateral Area Formula
To comprehend the lateral area formula notion, students must look at a few instances.
- Example 1:
A cuboid has dimensions of 6 units in length, 2 units in width, and 16 units in height. Determine the cuboid’s lateral surface area.
To locate the Cuboid’s lateral formula and the cube’s side length
The cuboid’s length is six units.
Cuboid width equals two units.
The cuboid’s height is 16 units.
Cube lateral area equals cuboid lateral area.
Using the cuboid’s lateral area formula,
Cuboid’s lateral area is equal to 2(length + breadth) 2(6 + 2) 16 = 256 units.
- Example 2: A sphere’s radius is four units. It is divided into two equally sized parts. Apply the lateral area formula to determine the lateral surface areas of both objects.
To locate the Surface area of the sphere’s and hemisphere’s sides
Given: The sphere and hemisphere’s radius is four units.
The sphere’s lateral area is calculated using the formula: Lateral area = 4r2 = 4 (4)2 = 201.142 square units.
Hemisphere’s lateral/curved surface area = 2r2 = 2 (4)2 = 100.571 square units
The sphere’s lateral area is 201.142 square units, while the hemisphere’s lateral/curved surface area is 100.571 square units.
- Example 3: Using the formula for lateral area, calculate the cube’s lateral area whose side is 7 units.
Find the cube’s lateral area.
Due to this: the cube side equals seven units
Using the cube’s lateral area formula, cube = 4a2 = 4 * 7 * 7, we can get 196.
The answer is that a cube’s lateral area is 196 square units.
FAQs (Frequently Asked Questions)
1. When Is Using a Curved Surface Area Recommended?
The area of a 3D figure that is merely curved is referred to as the curved surface area. In general, the relevance of the lateral surface area and the curved surface area is equal. For the cuboid, for instance, one uses the lateral surface area, but for the cylinder, when the top and base surfaces are not included, one can use the curved surface area.
2. How are the areas calculated?
To calculate the area of a rectangle or square, multiply its height by its width. This method is the simplest and most prominent. Since each side of a square is the same length, all students need to do to get the area is to multiply the length of one of the sides.