Volume of a Sphere Formula
The formula for calculating the volume of a sphere is given by:
V = (4/3) * π * r^3
where V is the volume and r is the radius of the sphere
The formula for calculating the volume of a sphere is given by:
V = (4/3) * π * r^3
where V is the volume and r is the radius of the sphere.
To understand this formula, let’s break it down step by step.
1. π (Pi): This is a mathematical constant, approximately equal to 3.14159. It is used to relate the circumference of a circle to its diameter or radius.
2. r: This represents the radius of the sphere, which is the distance from the center of the sphere to any point on its surface. It is a straight line segment.
3. r^3: This means raising the radius to the power of 3, which is equivalent to multiplying the radius by itself three times. For example, if the radius is 2, then r^3 would be 2 * 2 * 2 = 8.
4. (4/3): This is a rational number equal to 1.33333…, which is approximately 1.333. It is a fraction used to adjust for the relative volume of a sphere compared to a cube with the same diameter.
By multiplying the radius by itself three times, multiplying it by the constant π, and then multiplying the result by (4/3), we can obtain the volume of the sphere.
Let’s do an example:
Example: Calculate the volume of a sphere with a radius of 5 units.
Using the formula: V = (4/3) * π * r^3
V = (4/3) * 3.14159 * (5^3)
V = (4/3) * 3.14159 * 125
V ≈ 523.5988 cubic units
Therefore, the volume of the sphere is approximately 523.5988 cubic units.
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