Back To Course

High School Trigonometry: Homework Help Resource30 chapters | 203 lessons

Are you a student or a teacher?

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Jennifer Beddoe*

A sphere is a perfectly round three-dimensional object. This lesson will give a mathematical definition of a sphere, discuss the formulas associated with spheres and finish with a quiz.

A **sphere** is a geometrical figure that is perfectly round, 3-dimensional and circular - like a ball. Geometrically, a sphere is defined as the set of all points equidistant from a single point in space. The distance from an outer point to the center of the sphere is the **radius**(*r*) and the maximum straight distance from one side of the sphere to another is the **diameter** (*d*).

A **hemisphere** is what you would call half a sphere, if you were to split a sphere down the middle.

A **great circle** of the sphere is a circle that has the same radius and center as the sphere itself.

A sphere is the geometrical figure that occupies the biggest space, but has the smallest surface area. In other words, when something needs to be as small as possible but still have a large volume, it takes the shape of a sphere. That is why a balloon is round when you blow it up. It wants to hold as much air as possible with the smallest amount of surface. This occurs quite often in nature - common examples include bubbles and water drops.

The planet Earth is called a **spheroid** because it is extremely close to being a sphere, but is not perfectly round. It is elongated a bit at the North and South poles.

Here are the most common formulas associated with a sphere:

The **volume** (*V*) of a sphere is the amount of 'stuff' that could fit inside the sphere. Usually, when discussing volume, it is in terms of a liquid or gas. An example would be, 'What is the volume of air that can fit inside a basketball?' The formula for volume is:

*V* = (4/3?*r*^3

**Surface area** is just what its name implies: it's the area of the surface of an object. So, if you could cut open the basketball from the previous example and lay its surface out flat, you could see the surface area? This is useful for determining how much material would be needed to cover the sphere in question. The formula for surface area is:

*SA* = 4?*r*^2

Using our formulas, let's take a look at some example problems using spheres:

1.) What is the volume of a ball with a radius of 6 inches? (We'll use 3.14 for pi and round our answer to the nearest .10.)

Since we are determining the volume, we use the equation:

*V* = (4/3) ?*r*^3

We know the radius - the rest is just simple math.

*V* = (4/3)(3.14)(6^3)

*V* = 904.3 in^3

2.) What is the surface area of a sphere whose radius is 3 ft? (Use 3.14 for pi and round your answer to the nearest .10.)

We know our formula for surface area is:

*SA* = 4?*r*^2

*SA* = (4)(3.14)(3^2)

*SA* = 113.04 ft^2

3.) What is the volume of a water drop if the diameter is 1.2 cm? (Use 3.14 for pi and round your answer to the nearest .10.)

This problem is a bit trickier, since we are given the diameter and not the radius. To find the radius, just divide the diameter in half. Then, you can use the equation for volume.

1.2/2 = 0.6cm

*V* = (4/3) ?*r*^3

*V* = (4/3)(3.14)(0.6^3)

*V* = 81.0 cm^3

A **sphere** is a geometrical figure that is perfectly round with no corners or edges. It is a 3-dimensional shape, and, using the given equations, it is not difficult to find the volume or surface area. The **volume**(*V*) of a sphere is the amount of 'stuff' that could fit inside the sphere. The formula for volume is:

*V* = (4/3) ?*r*^3

**Surface area** is just what its name implies. It's the area of the surface of an object. The formula for surface area is:

*SA* = 4?*r*^2

Spheres are found quite often in nature, since they are the perfect shape to fit a large volume in a small area. A **hemisphere** is what you would call half a sphere if you were to split a sphere down the middle. A **great circle** of the sphere is a circle that has the same radius and center as the sphere itself.

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackDid you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
8 in chapter 22 of the course:

Back To Course

High School Trigonometry: Homework Help Resource30 chapters | 203 lessons

- Trigonometric Ratios and Similarity 6:49
- Practice Finding the Trigonometric Ratios 6:57
- The Pythagorean Theorem: Practice and Application 7:33
- Finding Distance with the Pythagorean Theorem 6:54
- Trigonometry and the Pythagorean Theorem 4:14
- Perfect Square: Definition, Formula & Examples 2:55
- Solid Figures: Definition, Properties & Examples 4:20
- Sphere: Definition & Formulas 4:56
- What is a Triangle Pyramid? - Definition & Formula 4:56
- What is Trigonometry? - Functions, Formulas & Applications 5:17
- Go to Triangle Trigonometry: Homework Help

- GRE Information Guide
- Computer Science 310: Current Trends in Computer Science & IT
- Earth Science 105: Introduction to Oceanography
- Computer Science 331: Cybersecurity Risk Analysis Management
- Computer Science 336: Network Forensics
- Natural Resources & Environmental Impact
- World Literature: Drama Since the 20th Century
- Visual Art Since the 18th Century
- World Literature: Drama Through the 19th Century
- Defamation, Libel & Slander
- MEGA Test Score Information
- Study.com GRE Scholarship: Application Form & Information
- PHR Prep Product Comparison
- ILTS Prep Product Comparison
- CTEL Prep Product Comparison
- TASC Prep Product Comparison
- FSA Prep Product Comparison

- Developing Effective Literacy Intervention Programs
- Gods & Stories from West African Mythology
- What is a Hematology Test? - Common Tests & Interpretations
- Joint Probability: Definition, Formula & Examples
- First Responders in Network Forensics: Role & Purpose
- Using Scheduling Commands in Linux
- Organizational Adaptation Theory: Definition & Application
- Using Lists in Python
- Quiz & Worksheet - Special Populations in Education
- Quiz & Worksheet - Encouraging Parent Involvement in Literacy
- Quiz & Worksheet - Java Max & Min Value in Java
- Quiz & Worksheet - Work of Theodor Schwann
- Quiz & Worksheet - Teaching Students in Foster Homes
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies

- Worth Publishers Psychology: Online Textbook Help
- Molecular Biology: Help & Review
- TASC Science: Prep and Practice
- Principles of Marketing: Help and Review
- 9th Grade English: Help and Review
- Student Assessments & Evaluations
- Praxis Middle School Science: Linear Momentum
- Quiz & Worksheet - Evaluating History Through Different Lenses
- Quiz & Worksheet - Solving Functional Problems with the Pythagorean Theorem
- Quiz & Worksheet - Habituation in Children
- Quiz & Worksheet - The Neonatal Environment
- Quiz & Worksheet - Characteristics of Septal Defects of the Heart

- A Rose for Emily by William Faulkner: Summary, Theme & Analysis
- Agonist: Definition & Effect
- How Can I Help My Child Get Ready for the NAPLAN Test?
- Thesis Statement Lesson Plan
- Where Can I Find Free SAT Prep Classes?
- Average PSAT Score
- Anti-Bullying Programs & Organizations
- The New SAT Math Section
- NGSS Science & Engineering Practices
- AP Biology Exam Scoring Information
- Environmental Science Projects
- Anti-Bullying Programs & Organizations

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject