Surface Area Of A Sphere Formula

Surface Area Of A Sphere Formula

The space occupied by a sphere’s curved surface is known as its surface area. When examined as three-dimensional structures, circular forms resemble spheres. A globe or a soccer ball, as examples. In the article published about the Surface Area of a Sphere Formula on the Extramarks website and mobile application, students may learn the formula for calculating a sphere’s surface area, also called the Surface Area of a Sphere Formula, as well as how to calculate and implement it in real life.

For students of various other boards, notes and solutions for the Surface Area of a Sphere Formula are also available in Hindi. Comprehension of the Surface Area of a Sphere Formula is made easier with the help of these notes provided by Extramarks experts. The notes and solutions based on the Surface Area of a Sphere Formula have been prepared in accordance with and while pertaining to the NCERT Syllabus, emulating the structure of the NCERT books.

What is the Surface Area of a Sphere?

The Surface Area of a Sphere Formula is the space that the sphere’s outer surface occupies. A sphere is a circle in three dimensions. A circle is a two-dimensional (2D) form, but a sphere is a three-dimensional (3D) shape, which is the difference between the two. A Surface Area of a Sphere Formula is measured in square units. Students should look at the sphere shown on the Extramarks website in the Surface Area of a Sphere Formula notes and solutions, which displays a sphere’s centre, radius, and diameter.

Sphere Definition

A three-dimensional object having a circular form and no vertices or edges is called a sphere. These shapes’ radius, diameter, circumference, and volume are crucial components. A three-dimensional object with a sphere-like form. The sphere is described by its three axes, namely the x, y, and z axes. The primary distinction between a circle and a sphere is this. Unlike other 3D forms, a sphere has no vertices or edges. 

Each point on the sphere’s surface is equally spaced from the centre. As a result, the sphere’s centre and surface are always the same distance apart. The radius of the sphere is the name given to this distance. The planets, a ball, and a globe are all examples of spheres.

The notes and solutions based on the Surface Area of a Sphere Formula have been curated by Extramarks experts after great consideration and research on the past years’ question papers. The framework of the Surface Area of a Sphere Formula notes designed by Extramarks experts is very easy to understand and comprehend. The Surface Area of a Sphere Formula notes are extremely internet-compatible, and students can also download them for offline study and reference.

Derivation of Surface Area of Sphere

Since a sphere is spherical, students should connect it to a curved object, like a cylinder, to calculate its surface area. A cylinder is a form that combines flat and curved surfaces. Now, if the radius of a cylinder and a sphere are equal, the sphere can fit seamlessly within the cylinder. This indicates that the cylinder’s height and the sphere’s height are equal. Therefore, this height may also be thought of as the sphere’s diameter.

Consequently, the following relationship between a Surface Area of a Sphere Formula and a cylinder’s lateral surface area is given: 

The surface area of a sphere equals the lateral surface area of a cylinder 

A cylinder’s lateral surface area is equal to 2 RH, where r is the cylinder’s radius and h is its height. Assuming that the sphere fits into the cylinder completely, the height of the cylinder may alternatively be thought of as the sphere’s diameter. Consequently, it is possible to state that the height of the cylinder = the diameter of the sphere = 2r. Thus, the Surface Area of a Sphere Formula is the surface area of a sphere = 2rh, where ‘h’ can be substituted by the diameter or 2r. Therefore, the Surface Area of a Sphere Formula is 2rh = 2r(2r) = 4r2.

The notes and solutions based on the Surface Area of a Sphere Formula have been compiled by some of the top subject-matter experts working in collaboration with Extramarks to make learning easier and fun for students.

The Surface Area of a Sphere Formula notes and solutions are extremely student-friendly, dynamic, diverse and varied in nature. Experts make sure that the notes are updated according to the CBSE NCERT syllabus and pertain to the framework of the NCERT books. 

The Hindi version of the Surface Area of a Sphere Formula notes and solutions has been compiled by some of the most skilled translators at Extramarks. The Surface Area of a Sphere Formula solution can be used by students to take personal notes.

Formula of Surface Area of Sphere

The radius of the sphere affects the Surface Area of a Sphere Formula. In the event that the sphere’s surface area is S and its radius is r. The sphere’s surface area is thus written as Surface Area of a Sphere Formula = 4r2, where r is the sphere’s radius. 

The Surface Area of a Sphere Formula may be calculated as S = 4(d/2)2, where d is the sphere’s diameter.

The Surface Area of a Sphere Formula has been mentioned and highlighted in the notes and solutions for the Surface Area of a Sphere Formula provided by Extramarks experts. These notes and solutions based on the Surface Area of a Sphere Formula can be used by students for self-study purposes. The notes and solutions based on the Surface Area of a Sphere Formula also contain high-quality illustrations and diagrams to help students better understand the concepts clearly. Examples have been provided wherever needed throughout the solutions for the Surface Area of a Sphere Formula provided by Extramarks.

Surface Area of Sphere = 4πr2; where ‘r’ is the radius of the sphere.

Students can learn more in detail about the Surface Area of a Sphere Formula in the Surface Area of a Sphere Formula notes and solutions provided by the Extramarks experts. They can also download these notes on the Surface Area of a Sphere Formula and enjoy unlimited access to all study materials needed just by registering themselves on the Extramarks website and mobile application.

How to Calculate the Surface Area of Sphere?

The space filled by a sphere’s surface is known as its surface area. The Surface Area of a Sphere Formula may be used to get the sphere’s surface area. Below are the procedures for calculating a Surface Area of a Sphere Formula. 

To understand how to use the Surface Area of a Sphere Formula to get a sphere’s surface area, students can take a look at the example cited below:

 Example: Find the size of the surface area of a 9-inch-radius spherical ball. 

Step 1: Take note of the sphere’s radius. The ball’s radius in this instance is 9 inches.

Step 2: Since we already know that the surface area of a sphere is equal to 4r2, we can calculate it as follows: surface area of sphere = 4r2 = 4 3.14 92 = 4 3.14 81 = 1017.36. 

Step 3: The sphere’s surface area is 1017.36 in2 as a result.

The notes and solutions for the Surface Area of a Sphere Formula can be downloaded in high quality. The Surface Area of a Sphere Formula notes are also descriptive, comprehensive and detailed in nature. The notes and solutions based on the Surface Area of a Sphere Formula provide curated assessments to evaluate the progress of students.

Curved Surface Area of Sphere

Because a sphere only has one curved surface, its total surface area is determined by its curved surface area. The curved surface area of a sphere is equal to the entire surface area of the sphere, since there is no flat surface in a spherical sphere. Therefore, the equation for a sphere’s curved surface area is the curved surface area of sphere = 4r2; where r is the sphere’s radius.

Surface Area of Sphere Examples

Example 1: Calculate the surface area of a sphere whose radius is 20 feet. (Use π = 3.14). 

The sphere’s radius, denoted by the letter “r,” is 20 feet. 

The sphere’s surface area is equal to 4r2 or, 4202 feet2. The sphere’s surface measures, 5024 feet2.

Example 2: Calculate a sphere’s surface area given a radius of 6 units. 

The radius, given as “r,” is equal to 6 units. Therefore, let’s substitute r = 6 units as the value. 

The sphere’s surface area is 4r2 = 4 x x 62 = 4 x 3.14 x 36 = 452.16 unit2. 

∴ The sphere’s surface area is 452.16 unit2.

Example 3: State true or false. 

a.) A sphere is a circle in three dimensions. 

b.) Because a sphere has only one curved surface and only one flat surface, the curved surface area of a sphere equals the total surface area of the sphere. 

Solution: 

a.) A sphere is a three-dimensional version of a circle, it is true. 

b.) Since a sphere only has one curved surface, it is true that the curved surface area of a sphere equals the overall surface area of the sphere.