Learning Materials
Features
Discover
Think of a soccer ball. Think of a globe. These are round three-dimensional objects, the shape of which is known as a sphere. In this article, we will explore how to determine the surface area of a sphere.
Millions of flashcards designed to help you ace your studies
Sign up for freeWhat is Vaia?
How does Vaia help me study more efficiently?
Where can I find more explanations like this?
What's smart about Vaia's flashcards?
Can I create my own content on Vaia?
How does spaced repetition work in Vaia flashcards?
What can you do with flashcards in Vaia?
Is Vaia a science-based learning platform?
How do Vaia's smart learning plans support your exam prep?
Can you create your own study sets in Vaia?
What is Vaia?
How does Vaia help me study more efficiently?
Where can I find more explanations like this?
What's smart about Vaia's flashcards?
Can I create my own content on Vaia?
How does spaced repetition work in Vaia flashcards?
What can you do with flashcards in Vaia?
Is Vaia a science-based learning platform?
How do Vaia's smart learning plans support your exam prep?
Can you create your own study sets in Vaia?
Achieve better grades quicker with Premium
Geld-zurück-Garantie, wenn du durch die Prüfung fällst
Did you know that StudySmarter supports you beyond learning?
Review generated flashcards
Start learning or create your own AI flashcards
Team Surface Area of Sphere Teachers
First, let's visualize the components of a sphere. Consider congruent circles in three-dimensional space that all have the same point for their center. Taken together, these circles form a sphere. All points on the surface of the sphere are an equal distance from its center. This distance is the radius of the sphere.
In space, a sphere is the locus of all points that are at a given distance from a given point called its center.
Now suppose you are holding a perfectly spherical ball in your hand, and you want to tightly wrap it in paper. The surface area of the sphere can be thought of as the minimum amount of paper that would be required to completely cover its entire surface. In other words, the sphere's surface area is the space that covers the surface of the shape, measured with square units (i.e., m2, ft2, etc.)
Consider the following sphere with radius r:
Surface area of a sphere - Vaia Originals
The surface area, S, of the sphere with radius, r, is given by the following formula:
Suppose that instead of the radius, you are given the diameter of the sphere. Since the diameter is twice the length of the radius, we can simply substitute the value in the above formula. This would lead to:
So the surface area, S, of a sphere with diameter, d, is:
When a plane intersects a sphere so that it contains the center of the sphere, the intersection is called a great circle. In effect, a great circle is a circle contained within the sphere whose radius is equal to the radius of the sphere. A great circle separates a sphere into two congruent halves, each called a hemisphere.
For example, if we approximate the Earth's shape as spherical, then we can call the equator a great circle because it passes through the center and splits the Earth (approximately) into two halves.
Let us take a look at some examples related to surface area of spheres.
Find the surface area of a sphere of radius 5 ft.
Solution:
Find the surface area of a sphere given that the area of its great circle is 35 square units.
Solution:
Surface area of the sphere = 4πr2
Area of the great circle = πr2
We are given
πr2 = 35
Surface area of the sphere = 4πr2
= 4 × 35
= 140 square units
The surface area of a sphere is 616 ft2. Find its radius.
Solution:
Note: The radius must be a positive value, so we know that -7 is not the solution.
Sign up for free to gain access to all our flashcards.
What is the surface area of spheres?
The sphere's surface area is the space that covers the surface of the shape, measured with square units (m2, ft2, etc.). The surface area, S, of a sphere with radius, r, is given by the formula: S = 4πr2
What is the formula for calculating the surface area of sphere?
The surface area, S, of a sphere with radius, r, is given by the formula: S = 4πr2
At StudySmarter, we have created a learning platform that serves millions of students. Meet the people who work hard to deliver fact based content as well as making sure it is verified.
Lily Hulatt is a Digital Content Specialist with over three years of experience in content strategy and curriculum design. She gained her PhD in English Literature from Durham University in 2022, taught in Durham University’s English Studies Department, and has contributed to a number of publications. Lily specialises in English Literature, English Language, History, and Philosophy.
Get to know Lily
Gabriel Freitas is an AI Engineer with a solid experience in software development, machine learning algorithms, and generative AI, including large language models’ (LLMs) applications. Graduated in Electrical Engineering at the University of São Paulo, he is currently pursuing an MSc in Computer Engineering at the University of Campinas, specializing in machine learning topics. Gabriel has a strong background in software engineering and has worked on projects involving computer vision, embedded AI, and LLM applications.
Get to know Gabriel
Vaia is a globally recognized educational technology company, offering a holistic learning platform designed for students of all ages and educational levels. Our platform provides learning support for a wide range of subjects, including STEM, Social Sciences, and Languages and also helps students to successfully master various tests and exams worldwide, such as GCSE, A Level, SAT, ACT, Abitur, and more. We offer an extensive library of learning materials, including interactive flashcards, comprehensive textbook solutions, and detailed explanations. The cutting-edge technology and tools we provide help students create their own learning materials. StudySmarter’s content is not only expert-verified but also regularly updated to ensure accuracy and relevance.
Learn moreSave explanations to your personalised space and access them anytime, anywhere!
Sign up with Email Sign up with AppleBy signing up, you agree to the Terms and Conditions and the Privacy Policy of Vaia.
Already have an account? Log in
Sign up to highlight and take notes. It’s 100% free.
Explanations 
Textbooks 
Exams 
GCSE 
IGCSE 
AS 
A Level 
International A Level 
University Admissions Tests 
Flashcards 
Vaia AI 
Notes 
Study Plans 
Study Sets 
Find a job 
Find a degree 
Student Deals 
Magazine 
Mobile App 
