Surface Area of a Sphere Formula
The surface area of a sphere is the total area that covers its outer surface. This surface area depends on the radius, diameter, or circumference of the sphere.
Below are all the formulas for calculating the surface area of a sphere, with detailed explanations and examples for each method.
Formulas for the Surface Area of a Sphere
Using Radius:
If the radius
The surface area
Using Diameter:
If the diameter
The surface area
Using Circumference:
If the circumference
The surface area
In these formulas:
is the radius of the sphere is the diameter of the sphere, where is the circumference of the sphere, where (Pi) is approximately equal to 3.14159
Detailed Explanation of Each Formula
1 Formula for Surface Area Using Radius
The formula
Example 1: Calculating Surface Area with Radius
Problem: Find the surface area of a sphere with a radius of
Solution:
- Write down the formula:
. - Substitute
: . - Calculate
: . - Multiply:
(using ).
The surface area of the sphere is approximately
2 Formula for Surface Area Using Diameter
The formula
Example 2: Calculating Surface Area with Diameter
Problem: A sphere has a diameter of
Solution:
- Write down the formula:
. - Substitute
: . - Calculate
: . - Multiply:
.
The surface area of the sphere is approximately
3 Formula for Surface Area Using Circumference
The formula
Example 3: Calculating Surface Area with Circumference
Problem: A sphere has a circumference of
Solution:
- Write down the formula:
. - Substitute
: . - Calculate
: . - Approximate
: .
The surface area of the sphere is approximately
These examples demonstrate how to calculate the surface area of a sphere using different known measurements, whether it’s the radius, diameter, or circumference.