Understanding how to calculate the surface area of a sphere is a fundamental concept in geometry. This article will guide you through the process step by step using a specific formula.
Step 1: The Surface Area Formula
The surface area (SA) of a sphere can be calculated using the following formula:
\[ SA = 4 \cdot \pi \cdot r^2 \]
Where:
- \( r \) is the radius of the sphere.
- \( \pi \) (pi) is a mathematical constant approximately equal to 3.14159.
Step 2: Explain the Formula
- The term \( 4 \cdot \pi \cdot r^2 \) represents the total surface area of the sphere.
- \( 4 \) is a constant that relates to the geometry of the sphere.
- \( \pi \) is a constant that appears in formulas involving circles and spheres.
- \( r^2 \) indicates that the radius is squared, which means it is multiplied by itself.
Step 3: Insert Numbers as an Example
Let's consider a sphere with a radius (\( r \)) of 5 units.
Step 4: Calculate the Final Value
First, substitute the given value into the formula:
\[ SA = 4 \cdot \pi \cdot 5^2 \]
Calculate the radius squared:
\[ 5^2 = 25 \]
Then multiply by \( \pi \):
\[ 4 \cdot \pi \cdot 25 = 4 \cdot 3.14159 \cdot 25 \]
Simplify the multiplication:
\[ 4 \cdot 3.14159 \cdot 25 \approx 12.56636 \cdot 25 = 314.159 \]
Final Value
The surface area of a sphere with a radius of 5 units is approximately 314.16 square units.
