Calculating the volume of a sphere is a fundamental concept in geometry and is applicable in various fields such as physics, engineering, and everyday life. This article will guide you through the steps to find the volume of a sphere using the appropriate formula, including an example calculation.
Volume of a Sphere Formula
To calculate the volume (\( V \)) of a sphere, you can use the following formula:
\[ V = \dfrac{4}{3} \cdot \pi \cdot r^3 \]
Where:
- \( r \) is the radius of the sphere.
Explanation of the Formula
- The term \( \dfrac{4}{3} \) is a constant that comes from the derivation of the volume formula for a sphere.
- \( \pi \) is a mathematical constant approximately equal to 3.14159.
- \( r^3 \) represents the cube of the radius, which scales the volume based on the size of the sphere.
Step-by-Step Calculation
Let's go through an example to demonstrate how to use this formula.
Example: Calculating the Volume of a Sphere
1. Identify the given value:
- Radius of the sphere (\( r \)) = 5 units
2. Substitute the value into the volume formula:
\[ V = \dfrac{4}{3} \cdot \pi \cdot 5^3 \]
3. Calculate the cube of the radius:
\[ 5^3 = 125 \]
4. Substitute and simplify:
\[ V = \dfrac{4}{3} \cdot \pi \cdot 125 \]
5. Multiply the terms:
\[ V = \dfrac{500}{3} \cdot \pi \]
6. Calculate the final value using \( \pi \approx 3.14159 \):
\[ V \approx \dfrac{500}{3} \cdot 3.14159 \]
\[ V \approx 523.598 \text{ cubic units} \]
Final Volume
The volume of a sphere with a radius of 5 units is approximately 523.598 cubic units.
