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What do dice, ice cream crates, and building blocks for kids all have in common? These items are all illustrations of ideal cubes. All six sides of a cube, a three-dimensional structure, are squares. So how does one determine the size of a cube? To accomplish this, determine the object's volume. A solid three-dimensional form with six square faces or sides is called a cube. Here, we'll go through the concept of the cube formula in detail.
Table of ContentImportant Cube Formula
Solved Examples Using Cube Formula
Important Cube Formula
One of the five platonic solids, the cube is also referred to as a regular hexahedron. Also check the Basic Maths Formula
Volume of Cube
On the basis of the above characteristics, many formulae may be used to determine the cube's volume. Both the cube's diagonal measurement and side length may be used to determine it.
- The volume of a cube is equal to a3 cubic inches (based on side length), where an is the length of a cube's side.
- The volume of a cube (based on its diagonal) is equal to (√3×d3)/9 cubic inches, where d is its diagonal's length.
Lateral Area of Cube
The total of all side faces' areas makes up a cube's lateral area. A cube has 4 side faces, hence its lateral area is equal to the sum of the areas of all 4 side faces.
LSA of Cube = 4a2
where a is the side length
Total Area of Cube
The base area and the cube's vertical surfaces combined will make up the cube's total surface area. Since every face of the cube is made up of identical-sized squares, the surface area of the cube as a whole equals the surface area of one face multiplied by five. Thus, the following formula may be used to determine a cube's surface area:
Total Surface Area (TSA) of a Cube = 6a2
where a is the side length.
Diagonal of Cube
The shorter diagonals on a cube's square sides and the larger diagonals that go through its centre are of different lengths. One side's length may be multiplied by the square root of three to find the major diagonal of a cube, which is the one that passes through the centre.
Diagonal of a cube = a√3
Let's use a few solved instances to better grasp the cube formulae.
Solved Examples Using Cube Formula
The following are the solved examples using the cube formula:
Question 1: Find the cube's surface area and volume if the side length is 10 cm.
Solution:
Given that a cube's side is 10 cm
Consequently, by applying the cube's surface area and volume equations, we may write;
Surface Area = 6 × a²
= 6 × 10²
= 6 × 100
= 600 square cm
Also, Volume =
= a³
= 10³
= 1000 cubic cm
Question 2: Calculate the cube's overall surface area if each side is 25 inches long.
The side length of the cube, a = 25 in
Using the equation A = 6a2 for the cube's surface area
Put the values
A = 6 × 25 × 25 = 3750 square inches
The cube has a surface area of 3750 square inches.
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What Is Cube Formula?
We may determine a cube's surface area, diagonals, and volume using the cube formula. These are straightforward calculations that mostly depend on the cube's side or edge length as a single parameter.
What is s in Cube Formula?
How to Use the Cube Formula to Determine a Cube's Diagonal?
A cube's major diagonal, which passes through the centre, may be calculated by multiplying one side's length by the square root of 3. As a result, the cube's diagonal is equal to a3, where an is the cube's edge.
