We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : How to find the volume of a sphere

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

← Previous 1 2 3 4 Next →

Example Question #261 : Solid Geometry

A sphere with a radius of $\frac{7}{8}$ is cut out of a cube that has a side length of . What is the volume of the resulting figure?

Possible Answers:

24.19

20.04

24.12

22.01

Correct answer:

24.19

Explanation:

Since the cube is bigger, we will be subtracting the volume of the sphere from the volume of the cube.

Start by recalling how to find the volume of a sphere.

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

Plug in the given radius to find the volume.

$\text{Volume of Sphere}=\frac{4}{3}\pi(\frac{7}{8})^3=\frac{343}{384}\pi$

Next, recall how to find the volume of a cube:

$\text{Volume of Cube}=(\text{edge})^3$

Plug in the given side length to find the volume of the cube.

$\text{Volume of Cube}=3^3=27$

Finally, subtract the volume of the sphere from the volume of the cube.

$\text{Volume of Figure}=27-\frac{343}{384}\pi=24.19$

Make sure to round to places after the decimal.

Report an Error

Example Question #262 : Solid Geometry

A sphere with a radius of $\frac{2}{5}$ is cut out of a cube that has a side length of . What is the volume of the resulting figure?

Possible Answers:

24.49

25.82

20.10

26.73

Correct answer:

26.73

Explanation:

Since the cube is bigger, we will be subtracting the volume of the sphere from the volume of the cube.

Start by recalling how to find the volume of a sphere.

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

Plug in the given radius to find the volume.

$\text{Volume of Sphere}=\frac{4}{3}\pi(\frac{2}{5})^3=\frac{32}{375}\pi$

Next, recall how to find the volume of a cube:

$\text{Volume of Cube}=(\text{edge})^3$

Plug in the given side length to find the volume of the cube.

$\text{Volume of Cube}=3^3=27$

Finally, subtract the volume of the sphere from the volume of the cube.

$\text{Volume of Figure}=27-\frac{32}{375}\pi=26.73$

Make sure to round to places after the decimal.

Report an Error

Example Question #31 : How To Find The Volume Of A Sphere

A sphere with a radius of $\frac{6}{5}$ is cut out of a cube that has a side length of . What is the volume of the resulting figure?

Possible Answers:

117.76

114.41

111.09

102.38

Correct answer:

117.76

Explanation:

Since the cube is bigger, we will be subtracting the volume of the sphere from the volume of the cube.

Start by recalling how to find the volume of a sphere.

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

Plug in the given radius to find the volume.

$\text{Volume of Sphere}=\frac{4}{3}\pi(\frac{6}{5})^3=\frac{288}{125}\pi$

Next, recall how to find the volume of a cube:

$\text{Volume of Cube}=(\text{edge})^3$

Plug in the given side length to find the volume of the cube.

$\text{Volume of Cube}=5^3=125$

Finally, subtract the volume of the sphere from the volume of the cube.

$\text{Volume of Figure}=125-\frac{288}{125}\pi=117.76$

Make sure to round to places after the decimal.

Report an Error

Example Question #32 : How To Find The Volume Of A Sphere

A sphere with a radius of $\frac{8}{3}$ is cut out of a cube that has a side length of . What is the volume of the resulting figure?

Possible Answers:

122.45

136.57

134.59

129.05

Correct answer:

136.57

Explanation:

Since the cube is bigger, we will be subtracting the volume of the sphere from the volume of the cube.

Start by recalling how to find the volume of a sphere.

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

Plug in the given radius to find the volume.

$\text{Volume of Sphere}=\frac{4}{3}\pi(\frac{8}{3})^3=\frac{2048}{81}\pi$

Next, recall how to find the volume of a cube:

$\text{Volume of Cube}=(\text{edge})^3$

Plug in the given side length to find the volume of the cube.

$\text{Volume of Cube}=6^3=216$

Finally, subtract the volume of the sphere from the volume of the cube.

$\text{Volume of Figure}=216-\frac{2048}{81}\pi=136.57$

Make sure to round to places after the decimal.

Report an Error

Example Question #33 : How To Find The Volume Of A Sphere

A sphere with a radius of $\frac{9}{2}$ is cut out of a cube that has a side length of . What is the volume of the resulting figure?

Possible Answers:

195.56

144.17

130.30

156.89

Correct answer:

130.30

Explanation:

Since the cube is bigger, we will be subtracting the volume of the sphere from the volume of the cube.

Start by recalling how to find the volume of a sphere.

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

Plug in the given radius to find the volume.

$\text{Volume of Sphere}=\frac{4}{3}\pi(\frac{9}{2})^3=\frac{243}{2}\pi$

Next, recall how to find the volume of a cube:

$\text{Volume of Cube}=(\text{edge})^3$

Plug in the given side length to find the volume of the cube.

$\text{Volume of Cube}=8^3=512$

Finally, subtract the volume of the sphere from the volume of the cube.

$\text{Volume of Figure}=512-\frac{243}{2}\pi=130.30$

Make sure to round to places after the decimal.

Report an Error

Example Question #31 : Spheres

True or false: A sphere with radius 1 has volume $\frac{4}{3} \pi$ .

Possible Answers:

True

False

Correct answer:

True

Explanation:

Given radius , the volume of a sphere can be calculated according to the formula

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

Set r = 1 :

$V = \frac{4}{3} \pi \cdot 1 ^{3}= \frac{4}{3} \pi \cdot 1= \frac{4}{3} \pi$

The statement is true.

Report an Error

Example Question #31 : How To Find The Volume Of A Sphere

What is the volume of a sphere with surface area 1,000 square centimeters?

Possible Answers:

$3,028 \; cm^{3}$

$2,974 \; cm^{3}$

$3,523 \; cm^{3}$

$3,532 \; cm^{3}$

$3,187 \; cm^{3}$

Correct answer:

$2,974 \; cm^{3}$

Explanation:

Use the surface area formula to find the radius, then use the volume formula to find the volume.

$A=4\pi r^{2}$

$4\pi r^{2} =1,000$

$r^{2} =\frac{1,000}{4\pi }=\frac{250}{\pi }$

$r =\sqrt{\frac{250}{\pi }}$

$V=\frac{4}{3} \pi r^{3} = \frac{4}{3} \pi \left (\sqrt{\frac{250}{\pi }} \right )^{3} \approx 2,974$

Report an Error

← Previous 1 2 3 4 Next →

View Tutors

Solomon
Certified Tutor

Endicott College, Bachelor in Business Administration, Liberal Arts and Sciences.

View Tutors

Mahmoud
Certified Tutor

New Mexico State University, Doctorate (PhD), Physics.

View Tutors

Vi
Certified Tutor

Mount carmael College, Bachelors, Psychology. Saint Louis University-Main Campus, PHD, Psychology.

All Intermediate Geometry Resources

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

Popular Subjects

Biology Tutors in Miami, Reading Tutors in Dallas Fort Worth, Math Tutors in Washington DC, MCAT Tutors in Miami, ACT Tutors in Dallas Fort Worth, Chemistry Tutors in New York City, ISEE Tutors in San Francisco-Bay Area, GRE Tutors in Miami, English Tutors in Houston, GRE Tutors in Los Angeles

Popular Courses & Classes

Spanish Courses & Classes in Phoenix, LSAT Courses & Classes in Denver, SSAT Courses & Classes in Houston, SSAT Courses & Classes in Philadelphia, Spanish Courses & Classes in Denver, SAT Courses & Classes in Phoenix, SSAT Courses & Classes in Miami, MCAT Courses & Classes in Philadelphia, Spanish Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Washington DC

Popular Test Prep

MCAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Houston, SAT Test Prep in New York City, MCAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Atlanta, SSAT Test Prep in Houston, LSAT Test Prep in Los Angeles, LSAT Test Prep in Atlanta, SAT Test Prep in San Francisco-Bay Area, ACT Test Prep in San Diego

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 : How to find the volume of a sphere

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #261 : Solid Geometry

Example Question #262 : Solid Geometry

Example Question #31 : How To Find The Volume Of A Sphere

Example Question #32 : How To Find The Volume Of A Sphere

Example Question #33 : How To Find The Volume Of A Sphere

Example Question #31 : Spheres

Example Question #31 : How To Find The Volume Of A Sphere

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: