Surface Area of Sphere
The surface area of a sphere is the area occupied by the surface of the sphere. Circular shapes are most likely to occur as a sphere when observed as threedimensional structures. For example, a globe or a soccer ball. In this lesson, you will learn how to calculate the surface area of a sphere. Since a sphere is threedimensional, you will also learn how to calculate its surface area and deduce the formula for it.
1.  What is the Surface Area of Sphere? 
2.  Derivation of Surface Area of Sphere 
3.  Formula of Surface Area of Sphere 
4.  How to Calculate the Surface Area of Sphere? 
5.  FAQs on Surface Area of Sphere 
What is Surface Area of a Sphere?
The area covered by the outer surface of the sphere is known as the surface area of a sphere. A sphere is a threedimensional solid object which has a round structure, like a circle. The difference between a sphere and a circle is that a circle is 2dimensional, whereas a sphere is a 3dimensional shape. The surface area of a sphere is the total area of the faces surrounding it. The surface area of sphere is given in square units.
Derivation of Surface Area of Sphere
It was found by Archimedes, that if the radius of cylinder and sphere is "r", the surface area sphere is equal to the lateral surface area of cylinder. Hence, the relation between the surface area of a sphere and lateral surface area of a cylinder is given as:
Surface Area of Sphere = Lateral Surface Area of Cylinder
⇒ The surface area of Sphere = 2πrh
In this case, height of cylinder = diameter of sphere = 2r
Hence, surface area of sphere is 2πrh = 2πr(2r) = 4πr^{2} square units.
Formula of Surface Area of Sphere
The formula of the surface area of the sphere depends on the radius of the sphere. If the radius of the sphere formed is r and the surface area of the sphere is S. Then, the surface area of the sphere is given by:
Surface Area of Sphere, S = 4πr^{2}
In terms of diameter, the surface area of a sphere is given as S = 4π(d/2)^{2}
where d is the diameter of the sphere.
How to Calculate Surface Area of Sphere?
The surface area of a sphere is the space occupied inside a sphere. The surface area of the sphere can be calculated using the formula of the surface area of the sphere. The steps to calculate the surface area of a sphere is:
 Step 1: Know the radius of the sphere.
 Step 2: Take the square of the radius by multiplying it by itself.
 Step 3: Multiply r^{2} by 4.
 Step 4: Multiply the value of 4r^{2} by the approximate value of pi, that is, 3.14.
 Step 5: At last, add the units to the final answer.
Let us take an example to learn how to calculate the surface area of a sphere using its formula.
Example: Find the surface area of a spherical ball having a radius of 9 inches.
Solution: Given, The radius of the basketball is 9 inches
As we know, the surface area of sphere = 4πr^{2}
r^{2} = 9^{2}= 81
Thus, surface area = 4πr^{2} = 4^{ }× π × r^{2} = 4 × π × 81 = 1017.36
⇒ S = 1017.36 in^{2}
∴ The surface area of the sphere is 1017.36 in^{2}.
Solved Examples on Surface Area of Sphere

Example 1: A stunt pilot is flying an airplane around the center of a sphere of radius 20 feet and forms a circle. Determine the surface area of the sphere. (Use π = 3.14).
Solution: Given, the radius r of the sphere is 20 feet.
The surface area of the sphere = 4πr^{2 }= 4 × π × 20^{2} = 5024 feet^{2}
∴ The surface area of the sphere is 5024 feet^{2} 
Example 2: The crosssection of a rubber ball has an outer diameter of 22 inches. The thickness of the rubber is 0.5 inches. What is the area of the inside surface of the ball to the nearest sq. inches? (Use π = 3.14).
Solution: Given the outer diameter = 22 inches and thickness = 0.5 inch
⇒ Thus, outer radius = 22/2 inches = 11 inches
Inner radius = Outer radius  Thickness = 11  0.5 = 10.5 inches
Inner surface area of the ball = 4πr^{2} = 4 × π × (10.5)^{2} = 4 × π × 110.25 = 1384.74 inch^{2}∴ The area of inside surface of the ball is 1384.74 square inches.
FAQs on Surface Area of Sphere
Why is the Surface Area of a Sphere 4 Times the Area of a Circle?
A string that completely covers the surface area of a sphere can completely cover the area surface of exactly four circles. This way you can check that the surface area of a sphere is four times the area of a circle. When we write the formula for the surface area of a sphere, we write the surface area of a sphere = 4πr^{2 }= 4(πr^{2}) = 4 × area of a circle.
How Many Sides and Vertices Does a Sphere Have?
A sphere is a threedimensional shape that is round like a circle. Hence, it has no sides, vertices, or faces.
Does a Sphere have Infinite Faces?
No, a sphere has no face. A face is a flat surface and a sphere has no flat surface. This makes the sphere a faceless threedimensional shape.
What is the Curved Surface Area and Total Surface Area of a Sphere?
A sphere has just one surface only and that too curved. In the absence of a flat surface in a sphere, the curved surface area of a sphere is equal to its total surface area of the sphere which is 4πr^{2}.
What is the Ratio of the Surface Area of the Sphere to the Volume of the Sphere of Unit Radius?
As we know, the formula of volume of a sphere is (4/3)πr^{3}, and the formula of the surface area of the sphere is 4πr^{2}. Thus, the ratio of the surface area of a sphere to the volume of a sphere of unit radius is given as (4π)/(4/3)π = 3:1.
How Does the Surface Area of Sphere Change When the Radius of Sphere is Halved?
The surface area of the sphere gets onefourth when the radius is halved as r = r/2. As, surface area of sphere = 4πr^{2} = 4π(r/2)^{2} = πr^{2 }= surface area/4. Thus, the surface area of the sphere gets onefourth as soon as its radius gets halved.