Lateral Area Formula
The lateral area formula is used to find the lateral area of any solid object. The lateral area of any figure is the area of the non-base faces only. Lateral area formulas help in calculating the lateral surface area of different figures including cuboid, cube, cylinder, cone, and sphere. Let us see more about the lateral area formulas along with a few solved examples.
What Is the Lateral Area Formula?
The lateral area formula for different types of objects is different. Hence there are many lateral area formulas which are explained below. The lateral area does not include the base area of the object as well as the face parallel to the base. The lateral area formula for various objects are given in the tabular list below:
List of Lateral Area Formula
We measure the lateral surface area for 3-dimensional shapes. Given below is a detailed tabular list for you to understand the lateral surface area formula.
| Shape | Lateral (curved) Surface Area |
| Cube | 4(side)2 |
| Cuboid | 2height (length+ breadth) |
| Cone | πrl |
| Cylinder | 2πrh |
| Hemisphere | 2 π r2 |
| Prism | base perimeter × height |
| Pyramid | (1/2) base Perimeter × slant height |
Examples on Lateral Area Formula
Let us take a look at a few examples to understand the lateral area formula concept
Example 1: The length, breadth, and height of a cuboid are 6 units, 2 units, and 16 units respectively. Calculate the lateral surface area of the cuboid.
Solution:
To find: Lateral formula of cuboid, length of the side of a cube
Given:
Length of cuboid = 6 units
Breadth of cuboid = 2 units
Height of cuboid = 16 units
Lateral area of cube = Lateral area of a cuboid
Using lateral area formula of cuboid,
Lateral area of cuboid = 2(length + breadth) × height
= 2( 6 + 2 ) × 16
= 256 units
Answer: Lateral area of cuboid = 256 units
Example 2: The radius of a sphere measures 4 units. This sphere is cut into two equal halves. Calculate the lateral surface areas of both objects by using the lateral area formula.
Solution:
To find: Lateral surface area of sphere and hemisphere
Given: Radius of the sphere and hemisphere = 4 units
Using lateral area formula,
Lateral area of sphere = 4πr2
= 4 × π × (4)2
= 201.142 square units
Lateral/ curved surface area of hemisphere = 2πr2
= 2 × π × (4)2
= 100.571 square units
Answer: Lateral area of sphere = 201.142 square units, and Lateral/ curved surface area of hemisphere = 100.571 square units
Example 3: Find the lateral area of the cube using the lateral area formula whose side is 7 units.
Solution:
To find: lateral area of a cube
Given that: side of a cube = 7 units
Using lateral area formula of cube = 4a2
= 4 * 7 * 7 = 196.
Answer: The lateral area of a cube is 196 square units.
FAQs on Lateral Area Formulas
What Is the Lateral Area Formula of Cone?
The lateral area formula for cone is LSA = πrl. Where r is the radius of a cone, l is the slant height of the cone, and π (pi) is a constant term with a value of 3.14 or 22/7.
What Is the Lateral Area Formula of Sphere?
The lateral surface area of sphere is expressed as LSA = 2πrh or 4πr2 (If a diameter of sphere = 2r). Where r is the radius of a sphere, h is the height of the sphere, and π (pi) is a constant term with a value of 3.14 or 22/7.
What Is the Lateral Area Formula of Cylinder?
The lateral surface area of cylinder is expressed as LSA = 2πrh. Where r is the radius of a circular base of the cylinder, h is the height of the cylinder, and π (pi) is a constant term with a value of 3.14 or 22/7.
What Is the Lateral Area Formula of Cuboid?
The lateral surface area of cuboid is expressed as LSA = 2h (l+b). Where l, b, and h are the length, breadth, and height of a cuboid.
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