Back To Course

High School Trigonometry: Homework Help Resource30 chapters | 203 lessons

Watch short & fun videos
**Start Your Free Trial Today**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 55,000 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

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 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

- MTEL Sheltered English Immersion: Practice & Study Guide
- C (ASCP) Technologist in Chemistry: Study Guide & Exam Prep
- MLT (ASCP) Medical Laboratory Technician: Study Guide & Exam Prep
- Pennsylvania Grades 4-8 Core Assessment - Mathematics & Science (5155): Study Guide & Test Prep
- Literary Elements Lesson Plans & Resources
- Teaching Basic Reading Skills to English Language Learners
- Standards-Based Learning for MA ELL Students
- Instructional Strategies for Teaching Academic Language
- Second Language Acquisition in ELL Classrooms
- Encouraging Listening & Speaking Skills Development in ELL Classrooms
- California Code of Regulations for Schools
- WV Next Generation Standards for Math
- Continuing Education Opportunities for Microbiology Technologists
- Professional Publications in Literacy
- Dyslexia Programs in Texas
- Study.com's Teacher Edition
- Study.com School Plans

- Ocean Invertebrates: Sponges & Cnidarians
- Manures & Fertilizers: Types, Uses & Examples
- What Is a Service Business?
- How to Convert Meters per Second to Miles per Hour
- The Case of Lady Sannox: Summary, Characters & Setting
- The Bronze Age: Armor, Weapons & Warfare
- What is Crashing in Project Management? - Definition & Example
- Hemoglobin Testing: Purpose & Types
- Quiz & Worksheet - Characteristics of the Mod Subculture
- Quiz & Worksheet - Correlative Conjunctions
- Quiz & Worksheet - Rectification Definition
- Quiz & Worksheet - Lifelong Learning
- Quiz & Worksheet - Biological Assimilation of Food
- Graphs & Charts in Everyday Life Flashcards
- Interpreting & Analyzing Data Sets Flashcards

- CSET Math Subtest 3: Practice & Study Guide
- Amsco Geometry: Online Textbook Help
- NY Regents Exam - Earth Science: Tutoring Solution
- Precalculus Algebra: Certificate Program
- NY Regents Exam - Living Environment: Help and Review
- Holt United States History Chapter 6: Citizenship & the Constitution (1787-Present)
- HiSET: Measuring the Economy
- Quiz & Worksheet - Attitude Formation Theory
- Quiz & Worksheet - Color Psychology
- Quiz & Worksheet - Cardiac Preload
- Quiz & Worksheet - Characteristics of Nonrenewable Resources
- Quiz & Worksheet - The Chemical Properties of Matter

- Indian Ocean: Location, Facts & History
- What is a Test Plan in Software Testing? - Examples & Definition
- A Modest Proposal Lesson Plan
- Common Core State Standards in Wisconsin
- TASC Test Locations
- How to Pass the Life & Health Insurance Exam
- Online Training Courses with Certificates
- Geometry Math Games
- Gettysburg Address Lesson Plan
- Where Can I Find Credit Recovery Classes?
- Soccer Lesson Plan
- How to Learn a Foreign Language

Browse by subject