Class 9 - Surface Area of a Sphere | Definition, Formula, Examples

The surface area of a sphere is the region occupied by any spherical object in a three-dimensional plane. A sphere is among the most found shapes around us. You can see many spherical objects near you like balls, chapatis and so on. 

Learning how to measure the surface area of a sphere is a basic computational skill that helps us in real life too. For example, by calculating the surface area of a sphere we can easily estimate the quantity required to coat a spherical object. In this article, we’ve covered this topic in detail along with examples and the formula to find the surface area of a sphere. Before starting with the surface area of a sphere, let’s briefly understand the sphere and its related terms like radius and diameter used in measuring area of sphere.

Table of Contents

• What is a Sphere?
• What is the Surface Area of a Sphere
• Surface Area of a Sphere Formula
• How to Calculate the Surface Area of a Sphere
• Solved Examples on Surface Area of a Sphere

 

What is a Sphere?

A sphere is a circular three-dimensional solid shape that is round with the same distance from its center to every point on its surface. A sphere is similar to a circle but it is a three-dimensional shape, while a circle is two-dimensional. There are no edges, vertices, or flat faces on the circle. A sphere can be divided into two equal parts called hemi-sphere.

The keyterms related to sphere are radius (r) diameter (d) and center (c).

Radius (r) of a sphere is the distance from the center to any point on the surface that stays the same.
Diameter (d) of a sphere is the total distance covered by a line starting from one point on spher to the other while passing throught the center d = 2 x r

 

What is the Surface Area of a Sphere

The total surface area of a sphere is the amount of area covered inside the sphere. It is denoted by letter ‘A’ and can be calculated using the surface area of the sphere formula. The surface area of a sphere depends on the square of the radius. Radius, and diameter are two important terms used for calculating the area of a sphere using the formula.
The surface area of a sphere of radius r = 4 times the area of a circle of radius r = 4 × (π r²)
So, Surface Area of a Sphere = 4 π r²

Surface Area of a Sphere Formula

The formula for the total surface area of a sphere is: A = 4πr², where r is the sphere's radius and π is about 3.14159. The total surface area and the curved surface area of a sphere are the same because a sphere only has one surface that is curved. Both are equal to 4πr².

How to Calculate the Surface Area of a Sphere

• To calculate the surface area of a sphere first, find the radius of the sphere by dividing its diameter by 2, that is, radius = d/2. 
• Then substitute in the formula: Surface Area = 4πr²
• For example, if d = 14 cm, then r = 7 cm and Surface Area = 4 × (22/7) × 49 = 616 cm².
  
  

Solved Examples on Surface Area of a Sphere

Example 1: Find the surface area of a sphere of radius 7 cm.
Solution: The surface area of a sphere of radius 7 cm would be:
A = 4πr = 4 × 22/7 × 7 × 7cm2
= 616 cm2

Example 2: Find (i) the curved surface area and (ii) the total surface area of a hemisphere of radius 21 cm.
Solution: The curved surface area of a hemisphere of radius 21 cm would be:
A= 2πr2 = 2 × 22/7 × 21 × 21 cm2

= 2772  cm2

Example 3: The hollow sphere, in which the circus motorcyclist performs his stunts, has a diameter of 7 m. Find the area available to the motorcyclist for riding.
Solution : Diameter of the sphere = 7 m. Therefore, radius is 3.5 m. So, the riding space available for the motorcyclist is the surface area of the ‘sphere’ which is
given by 4πr2 = 4 × 22/7 × 3.5 × 3.5m2
= 154m2