Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : Spheres

Study concepts, example questions & explanations for Intermediate Geometry

Create An Account

All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Spheres

A sphere has a circumference of $8\pi$ , what is its volume?

Possible Answers:

$\frac{196\pi}{3}$

$\frac{64\pi}{3}$

$48\pi$

$\frac{2048\pi}{3}$

$\frac{256\pi}{3}$

Correct answer:

$\frac{256\pi}{3}$

Explanation:

The circumference is given by $2\pi r$ which yields a radius of 4. The volume is given by $\frac{4}{3}\pi r^{3}$

Report an Error

Example Question #1 : Spheres

Possible Answers:

$\frac{1256}{3}\; \pi \; cm^3$

$98\pi\; cm^3$

$\frac{1372}{3}\; \pi \; cm^3$

$\frac{218}{3}\pi\; cm^3$

$\frac{196}{3}\pi\; cm^3$

Correct answer:

$\frac{1372}{3}\; \pi \; cm^3$

Explanation:

$\frac{4}{3}\cdot \pi \cdot r^3\rightarrow \frac{4}{3}\cdot \pi \cdot (7)^3$

Simplified, it is $\frac{1372}{3}\; \pi \; cm^3$

Report an Error

Example Question #3 : Spheres

What is the volume of a sphere with a diameter of 6 in?

Possible Answers:

$108\pi\ in^{3}$

$216\pi\ in^{3}$

$288\pi\ in^{3}$

$72\pi\ in^{3}$

$36\pi\ in^{3}$

Correct answer:

$36\pi\ in^{3}$

Explanation:

The formula for the volume of a sphere is:

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

where = radius. The diameter is 6 in, so the radius will be 3 in.

Report an Error

Example Question #1 : How To Find The Volume Of A Sphere

The circumference of a sphere is $27 \pi \:cm$ . What is the sphere's volume?

Possible Answers:

$10,403\:cm^3$

$82,488\:cm^3$

$10,308\:cm^3$

$9,983\:cm^3$

$10,306\:cm^3$

Correct answer:

$10,306\:cm^3$

Explanation:

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

Finding the volume is simple. All that we need is the radius!

The only information the problem provides is the circumference. In order to find the radius, we have to think how circumference relates to radius.

Since the equation for circumference is $C=\pi \cdot d$ , where d stands for diameter, and radius is half of the diameter, the two have diameter in common.

The first step in solving this problem is to determine the diameter from the circumference:

$C= \pi \cdot d$

$27 \cdot \pi = \pi \cdot d$

$\frac{27 \cdot \pi}{ \pi} = \frac{\pi \cdot d}{\pi}$

27 = d

Because the diameter is $27\:cm$ , the radius must be $13.5\:cm$ .

Now we are ready to solve for the volume after substituting in our value.

$V= \frac{4}{3} \cdot \pi \cdot (13.5)^3$

$V= \frac{4}{3} \cdot \pi \cdot (2,460.375)$

$V = 3280.5 \cdot \pi$

$V =10,305.99 \approx10,306\:cm^3$

Report an Error

Example Question #5 : Spheres

A cube with a side length of 20 inches has a sphere inscribed within. What is the volume of the sphere?

Possible Answers:

$V=3,330\hspace{1mm}in^3$

$V=2,500\hspace{1mm}in^3$

$V=4,189\hspace{1mm}in^3$

$V=1,509\hspace{1mm}in^3$

$V=5,239\hspace{1mm}in^3$

Correct answer:

$V=4,189\hspace{1mm}in^3$

Explanation:

The cube has a side length of 20 inches. Since the sphere is inscribed within the cube its diameter measures 20 inches; the radius will be 10 inches.

The volume of a sphere is given by

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

$V=\frac{4}{3}\pi (10)^3=\mathbf{4,189\hspace{1mm}in^3}$

Report an Error

Example Question #2 : Spheres

A sphere is cut in half as shown by the figure below.

If the radius of the sphere is , find the volume of the figure.

Possible Answers:

18.55

16.30

16.76

15.09

Correct answer:

16.76

Explanation:

Recall how to find the volume of a sphere:

$\text{Volume of Sphere}=\frac{4}{3}\pi\times\text{radius}^3$

Now since we only have half a sphere, divide the volume by .

$\text{Volume of Figure}=\frac{1}{2}(\frac{4}{3}\pi\times\text{radius})^2$

$\text{Volume of Figure}=\frac{2}{3}\pi\times\text{radius}^3$

Plug in the given radius to find the volume of the figure.

$\text{Volume of Figure}=\frac{2}{3}\pi(2)^3=\frac{16}{3}\pi=16.76$

Make sure to round to places after the decimal.

Report an Error

Example Question #3 : Spheres

A sphere is cut in half as shown by the figure below.

If the radius of the sphere is , what is the volume of the figure?

Possible Answers:

55.08

56.55

51.18

58.63

Correct answer:

56.55

Explanation:

Recall how to find the volume of a sphere:

$\text{Volume of Sphere}=\frac{4}{3}\pi\times\text{radius}^3$

Now since we only have half a sphere, divide the volume by .

$\text{Volume of Figure}=\frac{1}{2}(\frac{4}{3}\pi\times\text{radius})^2$

$\text{Volume of Figure}=\frac{2}{3}\pi\times\text{radius}^3$

Plug in the given radius to find the volume of the figure.

$\text{Volume of Figure}=\frac{2}{3}\pi(3)^3=18\pi=56.55$

Make sure to round to places after the decimal.

Report an Error

Example Question #242 : Solid Geometry

A sphere is cut in half as shown by the figure below.

If the radius of the sphere is , what is the volume of the figure?

Possible Answers:

134.04

151.03

144.07

125.09

Correct answer:

134.04

Explanation:

Recall how to find the volume of a sphere:

$\text{Volume of Sphere}=\frac{4}{3}\pi\times\text{radius}^3$

Now since we only have half a sphere, divide the volume by .

$\text{Volume of Figure}=\frac{1}{2}(\frac{4}{3}\pi\times\text{radius})^2$

$\text{Volume of Figure}=\frac{2}{3}\pi\times\text{radius}^3$

Plug in the given radius to find the volume of the figure.

$\text{Volume of Figure}=\frac{2}{3}\pi(4)^3=\frac{128}{3}\pi=134.04$

Make sure to round to places after the decimal.

Report an Error

Example Question #9 : How To Find The Volume Of A Sphere

A sphere is cut in half as shown by the figure below.

If the radius of the sphere is $\frac{1}{2}$ , what is the volume of the figure?

Possible Answers:

0.26

0.36

0.16

0.46

Correct answer:

0.26

Explanation:

Recall how to find the volume of a sphere:

$\text{Volume of Sphere}=\frac{4}{3}\pi\times\text{radius}^3$

Now since we only have half a sphere, divide the volume by .

$\text{Volume of Figure}=\frac{1}{2}(\frac{4}{3}\pi\times\text{radius})^2$

$\text{Volume of Figure}=\frac{2}{3}\pi\times\text{radius}^3$

Plug in the given radius to find the volume of the figure.

$\text{Volume of Figure}=\frac{2}{3}\pi(\frac{1}{2})^3=\frac{1}{12}\pi=0.26$

Make sure to round to places after the decimal.

Report an Error

Example Question #4 : Spheres

A sphere is cut in half as shown by the figure below.

If the radius of the sphere is , what is the volume of the figure?

Possible Answers:

288.09

230.36

212.20

261.80

Correct answer:

261.80

Explanation:

Recall how to find the volume of a sphere:

$\text{Volume of Sphere}=\frac{4}{3}\pi\times\text{radius}^3$

Now since we only have half a sphere, divide the volume by .

$\text{Volume of Figure}=\frac{1}{2}(\frac{4}{3}\pi\times\text{radius})^2$

$\text{Volume of Figure}=\frac{2}{3}\pi\times\text{radius}^3$

Plug in the given radius to find the volume of the figure.

$\text{Volume of Figure}=\frac{2}{3}\pi(5)^3=\frac{250}{3}\pi=261.80$

Make sure to round to places after the decimal.

Report an Error

View Tutors

Nicole
Certified Tutor

Western Governors University, Bachelor of Education, Special Education.

View Tutors

Sharif
Certified Tutor

NCCU, Bachelors, Physics and Mathematics.

View Tutors

Alejandro
Certified Tutor

Kennesaw State University, Bachelor of Science, Computer Software Engineering.

All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Physics Tutors in New York City, Algebra Tutors in San Francisco-Bay Area, SSAT Tutors in Boston, Math Tutors in Chicago, SSAT Tutors in Atlanta, SAT Tutors in Atlanta, GRE Tutors in Phoenix, Spanish Tutors in Washington DC, LSAT Tutors in Miami, Biology Tutors in Boston

Popular Courses & Classes

SSAT Courses & Classes in Philadelphia, GMAT Courses & Classes in Seattle, LSAT Courses & Classes in Los Angeles, MCAT Courses & Classes in Chicago, LSAT Courses & Classes in Washington DC, MCAT Courses & Classes in San Diego, MCAT Courses & Classes in Philadelphia, SSAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Denver, ISEE Courses & Classes in San Francisco-Bay Area

Popular Test Prep

LSAT Test Prep in Washington DC, MCAT Test Prep in San Diego, MCAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Los Angeles, SSAT Test Prep in Washington DC, MCAT Test Prep in Denver, SAT Test Prep in Chicago, LSAT Test Prep in Los Angeles, SSAT Test Prep in Chicago, GRE Test Prep in New York City

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

Intermediate Geometry : Spheres

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1 : Spheres

Example Question #1 : Spheres

Example Question #3 : Spheres

Example Question #1 : How To Find The Volume Of A Sphere

Example Question #5 : Spheres

Example Question #2 : Spheres

Example Question #3 : Spheres

Example Question #242 : Solid Geometry

Example Question #9 : How To Find The Volume Of A Sphere

Example Question #4 : Spheres

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: