Call Now to Set Up Tutoring:

(888) 888-0446

Pre-Algebra : Volume of a Sphere

Study concepts, example questions & explanations for Pre-Algebra

Create An Account

All Pre-Algebra Resources

11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Volume Of A Sphere

A certain children's basketball has a diameter of 6 inches. What is the volume of the basketball?

Possible Answers:

$18\pi in.^{3}$

$36\pi in.^{3}$

$9\pi in.^{3}$

$108\pi in.^{3}$

$288\pi in.^{3}$

Correct answer:

$36\pi in.^{3}$

Explanation:

Math involves a lot of formulas. Unfortunately that means we either have to do some memorization or compile a really long list of formulas for reference. Either way, a basketball is a sphere, which means we have to know the formula for the volume of a sphere to solve this problem.

$V=\frac{4}{3}\pi r^{3}$

stands for volume, and stands for radius. Therefore, all we need to do is plug in the radius of the basketball and do a little calculation to find our answer. The problem is that we do not have the radius. All we have is a diameter. But if we remember the relationship between diameters and radii (the plural of radius), we have nothing to fear. The diameter is just twice as long as the radius. That means that if our diameter is 6 inches, the radius is simply 3 inches. Now that we have our radius, we are ready to plug and play.

$V=\frac{4}{3}\pi (3)^{3}=\frac{4}{3}\pi(27)=36\pi$

Since our original unit was inches, and volume is always expressed in cubic units, our final answer is

$36\pi in.^3$

Report an Error

Example Question #1 : Volume Of A Sphere

In terms of $\pi$ , give the volume, in cubic inches, of a spherical water tank with a diameter of 20 feet.

Possible Answers:

$230,400 \pi\textrm{ in}^{3}$

$2,304,000 \pi \textrm{ in}^{3}$

$18,432,000\pi\textrm{ in}^{3}$

$307,200\pi\textrm{ in}^{3}$

$57,600 \pi\textrm{ in}^{3}$

Correct answer:

$2,304,000 \pi \textrm{ in}^{3}$

Explanation:

20 feet = $20 \times 12 = 240$ inches, the diameter of the tank; half of this, or 120 inches, is the radius. Set r = 120 , substitute in the volume formula, and solve for :

$V = \frac{4}{3} \pi r^{3}$

$V = \frac{4}{3} \pi \cdot 120^{3}$

$V = \frac{4}{3} \pi \cdot 1,728,000$

$V = 2,304,000 \pi$ cubic inches

Report an Error

Example Question #2 : Volume Of A Sphere

A sphere has diameter 3 meters. Give its volume in cubic centimeters (leave in terms of $\pi$ ).

Possible Answers:

$3,375,000\pi \textrm{ cm}^{3}$

$36,000,000\pi \textrm{ cm}^{3}$

$4,500,000\pi \textrm{ cm}^{3}$

$1,125,000\pi \textrm{ cm}^{3}$

$27,000,000\pi \textrm{ cm}^{3}$

Correct answer:

$4,500,000\pi \textrm{ cm}^{3}$

Explanation:

The diameter of 3 meters is equal to $3 \times 100 = 300$ centimeters; the radius is half this, or 150 centimeters. Substitute r = 150 in the volume formula:

$V= \frac{4}{3} \pi r^{3}$

$V= \frac{4}{3} \cdot \pi \cdot 150^{3}$

$V= \frac{4}{3} \cdot 150 \cdot 150 \cdot 150\cdot \pi$

$V= 4,500,000\pi$ cubic centimeters

Report an Error

Example Question #3 : Volume Of A Sphere

A car dealership wants to fill a large spherical advertising ballon with helium. It can afford to buy 1,000 cubic yards of helium to fill this balloon. What is the greatest possible diameter of that balloon (nearest tenth of a yard)?

Possible Answers:

$15.4 \;\textrm{yd}$

$7.7 \;\textrm{yd}$

$6.2 \;\textrm{yd}$

$12.4 \;\textrm{yd}$

$9.3 \;\textrm{yd}$

Correct answer:

$12.4 \;\textrm{yd}$

Explanation:

The volume of a sphere, given its radius, is

$V = \frac{4\pi r^{3}}{3}$

Set V = 1,000 , solve for , and double that to get the diameter.

$1,000= \frac{4\pi r^{3}}{3}$

$r^{3} = \frac{1,000 \cdot 3 }{4\pi} \approx 238.7$

$r \approx \sqrt[3]{238.7} \approx 6.2$

The diameter is twice this, or 12.4 yards.

Report an Error

Example Question #1 : Volume Of A Sphere

The diameter of a sphere is . What is the volume of the sphere?

Possible Answers:

$\frac{33}{4}\pi$

$\frac{32}{3}\pi$

$\frac{18}{7}\pi$

$32\pi$

$\frac{16}{3}\pi$

Correct answer:

$\frac{32}{3}\pi$

Explanation:

The formula for finding volume of a sphere is:

$V = \frac{4}{3}\pi r^{3}$

We are given the diameter, so to find radius we divide the diameter by :

$4\div2 = 2$

We plug this radius into the formula:

$V = \frac{4}{3}\pi \left ( 2^{3}\right )$

$V = \frac{4}{3}\pi \left ( 8\right )$

$V = \frac{32}{3}\pi$

Report an Error

Example Question #2 : Volume Of A Sphere

A hollow sphere has a diameter of 8 inches from the center of the sphere to the outermost shell. The shell of the sphere is 1 inch thick. What is the volume of the shell or wall of the sphere?

Possible Answers:

V=268.1in^3

V=56in^3

V=179.6in^3

V=89 in^3

V=192.4in^3

Correct answer:

V=89 in^3

Explanation:

The questions asks the volume of the wall of the sphere only. Therefore it is necessary to find the total volume of the large sphere and subtract the volume of the inner sphere (formed by the wall) from it.

Volume of large sphere:

$V=\frac{4}{3} \pi r^3=\frac{4}{3}\pi(4^3)=268.1in^3$

Volume of inner sphere:

$V=\frac{4}{3} \pi r^3=\frac{4}{3}\pi(3.5^3)=179.6in^3$

The difference between the two volumes leaves only the volume of the wall of the sphere:

268.1-179.6=89in^3

Report an Error

Example Question #4 : Volume Of A Sphere

Regulations for professional soccer state that the diameter of the ball must be 8.65 inches for a size 5 regulation ball. What is the volume of the soccer ball?

Possible Answers:

V=339in^2

V=339in^3

The answer is not present.

V=393in^3

V=933in^3

Correct answer:

V=339in^3

Explanation:

The volume of a sphere is given by $\frac{4}{3}\pi r^3$ . The problem listed the diameter of the ball. Half of this number is the radius.

$V=\frac{4}{3}\pi (4.325)^3=339in^3$

When using a calculator to solve these types of problems it is best to do the problem in chunks to avoid input errors. For instance find out what the value of the radius cubed is first. Then multiply the other terms.

The units of volume are always cubed, not squared.

Report an Error

Example Question #6 : Volume Of A Sphere

Michelle plays softball for her high school. She is the only pitcher on the team. She is the only player that is guaranteed to touch the ball on every play. The problem is, her hands are not big enough to get a grip on the ball because the ball is too big. What is the volume of the softball that has a diameter of 6 inches?

Possible Answers:

$288\pi inches^3$

$36\pi inches^2$

$48\pi inches^3$

$288\pi inches^2$

$36 \pi inches^3$

Correct answer:

$36 \pi inches^3$

Explanation:

The formula to find the volume of a sphere is $\frac{4}{3} * \pi * r^3$

Find the radius of the softball and substitute that in place of r.

Answer will be left in pi format.

4/3 = 1.33333333

r^3 = 3^3

r^3 = 27

1.33333333 * 27 = 36

$36\pi inches^3$

Report an Error

Example Question #3 : Volume Of A Sphere

Find the volume of a sphere with a diameter of .

Possible Answers:

$375\pi$

$\frac{500}{3}\pi$

$500\pi$

$\frac{100}{3}\pi$

$\frac{400}{3}\pi$

Correct answer:

$\frac{500}{3}\pi$

Explanation:

Write the formula to find the volume of a sphere.

$V=\frac{4}{3}\pi r^3$

Divide the diameter by two to obtain the radius. The radius is five.

Substitute the radius into the volume equation.

$V=\frac{4}{3}\pi (5)^3=\frac{4}{3}\pi (125) = \frac{500}{3}\pi$

Report an Error

Example Question #1 : Volume Of A Sphere

Find the volume of a sphere with a radius of $\pi$ .

Possible Answers:

$\frac{16}{3}\pi^4$

$\frac{7}{3}\pi$

$\frac{16}{9}\pi^4$

$\frac{4}{3}\pi^4$

$\frac{16}{9}\pi^3$

Correct answer:

$\frac{4}{3}\pi^4$

Explanation:

Write the formula for the volume of a sphere and substitute the radius.

$V=\frac{4}{3}\pi r^3=\frac{4}{3}\pi (\pi)^3=\frac{4}{3}\pi^4$

Report an Error

View Pre-Algebra Tutors

Anjali
Certified Tutor

Delhi University, Bachelor of Science, Physics. Kumuan University, Master of Science, Physics.

View Pre-Algebra Tutors

Arianna
Certified Tutor

Washington State University, Bachelor in Arts, Communication, General. City University of Seattle, Masters in Business Admini...

View Pre-Algebra Tutors

Ronald
Certified Tutor

Towson University, Master of Science, Counseling Psychology.

All Pre-Algebra Resources

11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in San Francisco-Bay Area, French Tutors in Seattle, Statistics Tutors in Houston, Computer Science Tutors in Seattle, GRE Tutors in Phoenix, French Tutors in Los Angeles, Physics Tutors in Houston, Reading Tutors in Boston, Chemistry Tutors in Philadelphia, Spanish Tutors in Philadelphia

Popular Courses & Classes

ISEE Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Washington DC, LSAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Atlanta, Spanish Courses & Classes in Los Angeles, SAT Courses & Classes in San Diego, SAT Courses & Classes in Washington DC, GMAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Washington DC, LSAT Courses & Classes in Chicago

Popular Test Prep

ACT Test Prep in Washington DC, SSAT Test Prep in New York City, ISEE Test Prep in Los Angeles, ACT Test Prep in Chicago, ACT Test Prep in Atlanta, MCAT Test Prep in Miami, MCAT Test Prep in Houston, LSAT Test Prep in Philadelphia, LSAT Test Prep in Houston, SAT Test Prep in Miami

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Pre-Algebra : Volume of a Sphere

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #1 : Volume Of A Sphere

Example Question #1 : Volume Of A Sphere

Example Question #2 : Volume Of A Sphere

Example Question #3 : Volume Of A Sphere

Example Question #1 : Volume Of A Sphere

Example Question #2 : Volume Of A Sphere

Example Question #4 : Volume Of A Sphere

Example Question #6 : Volume Of A Sphere

Example Question #3 : Volume Of A Sphere

Example Question #1 : Volume Of A Sphere

All Pre-Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: