Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : Solid Geometry

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 #11 : 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:

1120.30

1056.08

1098.67

1072.33

Correct answer:

1072.33

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.

$\text{Volume of Figure}=\frac{2}{3}\pi(8)^3=\frac{1024}{3}\pi=1072.33$

Make sure to round to places after the decimal.

Report an Error

Example Question #14 : 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 $\frac{1}{3}$ , what is the volume of the figure?

Possible Answers:

0.09

0.08

0.06

0.07

Correct answer:

0.08

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.

$\text{Volume of Figure}=\frac{2}{3}\pi(\frac{1}{3})^3=\frac{2}{81}\pi=0.08$

Make sure to round to places after the decimal.

Report an Error

Example Question #12 : 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:

1526.81

1613.25

1589.67

1540.20

Correct answer:

1526.81

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.

$\text{Volume of Figure}=\frac{2}{3}\pi(9)^3=486\pi=1526.81$

Make sure to round to places after the decimal.

Report an Error

Example Question #16 : 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 , what is the volume of the figure?

Possible Answers:

2032.70

2094.40

2100.03

2086.20

Correct answer:

2094.40

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.

$\text{Volume of Figure}=\frac{2}{3}\pi(10)^3=\frac{2000}{3}\pi=2094.40$

Make sure to round to places after the decimal.

Report an Error

Example Question #17 : 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 , what is the volume of the figure?

Possible Answers:

2787.64

2558.95

2633.32

2704.05

Correct answer:

2787.64

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.

$\text{Volume of Figure}=\frac{2}{3}\pi(11)^3=\frac{2662}{3}\pi=2787.64$

Make sure to round to places after the decimal.

Report an Error

Example Question #11 : Spheres

A sphere is cut in half and is then placed on top of a cylinder so they both share a base as shown by the figure below.

Find the volume of the figure.

Possible Answers:

1824.50

1811.21

1809.56

1804.26

Correct answer:

1809.56

Explanation:

In order to find the volume of the figure, we will first need to find the volumes of the cylinder and of the half sphere.

Recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

$\text{Volume of Cylinder}=\pi\times 6^2 \times 12=432 \pi$

Next, find the volume of the half sphere.

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

Plug in the radius to find the volume of the half sphere.

$\text{Volume of Half Sphere}=\frac{2}{3}\times\pi\times 6^3=144\pi$

Next, add up the two volumes together to find the volume of the figure.

$\text{Volume of Figure}=\text{Volume of Half Sphere}+\text{Volume of Cylinder}$

$\text{Volume of Figure}=432\pi + 144\pi=576\pi=1809.56$

Remember to round to places after the decimal.

Report an Error

Example Question #13 : Spheres

A sphere is cut in half and is placed on top of a cylinder so that they share the same base as shown by the figure below.

Find the volume of the figure.

Possible Answers:

3219.59

3058.29

3027.45

3190.21

Correct answer:

3027.45

Explanation:

In order to find the volume of the figure, we will first need to find the volumes of the cylinder and of the half sphere.

Recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

$\text{Volume of Cylinder}=\pi\times 7^2 \times 15=735\pi$

Next, find the volume of the half sphere.

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

Plug in the radius to find the volume of the half sphere.

$\text{Volume of Half Sphere}=\frac{2}{3}\times\pi\times 7^3=\frac{686}{3}\pi$

Next, add up the two volumes together to find the volume of the figure.

$\text{Volume of Figure}=\text{Volume of Cylinder}+\text{Volume of Half Sphere}$

$\text{Volume of Figure}=735\pi + \frac{686}{3}\pi=3027.45$

Remember to round to places after the decimal.

Report an Error

Example Question #14 : Spheres

A sphere is cut in half and placed on top of a cylinder so that they share the same base as shown by the figure below.

Find the volume of the figure.

Possible Answers:

590.24

536.17

544.12

526.89

Correct answer:

536.17

Explanation:

In order to find the volume of the figure, we will first need to find the volumes of the cylinder and of the half sphere.

Recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

$\text{Volume of Cylinder}=\pi\times 4^2 \times 8=128\pi$

Next, find the volume of the half sphere.

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

Plug in the radius to find the volume of the half sphere.

$\text{Volume of Half Sphere}=\frac{2}{3}\times\pi\times 4^3=\frac{128}{3}\pi$

Next, add up the two volumes together to find the volume of the figure.

$\text{Volume of Figure}=\text{Volume of Cylinder}+\text{Volume of Half Sphere}$

$\text{Volume of Figure}=128\pi + \frac{128}{3}\pi=536.17$

Remember to round to places after the decimal.

Report an Error

Example Question #21 : Spheres

A sphere is cut in half and placed on top of a cylinder so that they share the same base as shown by the figure below.

Find the volume of the figure.

Possible Answers:

618.32

650.12

679.05

636.70

Correct answer:

636.70

Explanation:

In order to find the volume of the figure, we will first need to find the volumes of the cylinder and of the half sphere.

Recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

$\text{Volume of Cylinder}=\pi\times 4^2 \times 10=160\pi$

Next, find the volume of the half sphere.

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

Plug in the radius to find the volume of the half sphere.

$\text{Volume of Half Sphere}=\frac{2}{3}\times\pi\times 4^3=\frac{128}{3}\pi$

Next, add up the two volumes together to find the volume of the figure.

$\text{Volume of Figure}=\text{Volume of Cylinder}+\text{Volume of Half Sphere}$

$\text{Volume of Figure}=160\pi + \frac{128}{3}\pi=636.70$

Remember to round to places after the decimal.

Report an Error

Example Question #251 : Solid Geometry

A sphere is cut in half and placed on top of a cylinder so that they share the same base as shown by the figure below.

Find the volume of the figure.

Possible Answers:

5333.56

5190.20

5294.63

4921.59

Correct answer:

5294.63

Explanation:

In order to find the volume of the figure, we will first need to find the volumes of the cylinder and of the half sphere.

Recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

$\text{Volume of Cylinder}=\pi\times 8^2 \times 21=1344\pi$

Next, find the volume of the half sphere.

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

Plug in the radius to find the volume of the half sphere.

$\text{Volume of Half Sphere}=\frac{2}{3}\times\pi\times 8^3=\frac{1024}{3}\pi$

Next, add up the two volumes together to find the volume of the figure.

$\text{Volume of Figure}=\text{Volume of Cylinder}+\text{Volume of Half Sphere}$

$\text{Volume of Figure}=1344\pi + \frac{1024}{3}\pi=5294.63$

Remember to round to places after the decimal.

Report an Error

View Tutors

Mort
Certified Tutor

Rensselaer Polytechnic Institute, Bachelor of Science, Electrical Engineering.

View Tutors

Daniel
Certified Tutor

Stony Brook University, Bachelors, Biology, General. SUNY College of Optometry, PHD, Optometry.

View Tutors

Daniela
Certified Tutor

University Of Monterrey, Bachelor of Education, Early Childhood Special Education. University of Monterrey, Diploma, Early Ch...

All Intermediate Geometry Resources

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

Popular Subjects

SSAT Tutors in Denver, ACT Tutors in Houston, LSAT Tutors in Phoenix, Physics Tutors in Miami, Computer Science Tutors in Boston, Chemistry Tutors in Phoenix, Reading Tutors in Atlanta, LSAT Tutors in New York City, LSAT Tutors in San Diego, English Tutors in Houston

Popular Courses & Classes

SSAT Courses & Classes in Seattle, MCAT Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Miami, SSAT Courses & Classes in Washington DC, LSAT Courses & Classes in Boston, SAT Courses & Classes in Denver, SSAT Courses & Classes in Philadelphia, SAT Courses & Classes in Miami, ISEE Courses & Classes in San Francisco-Bay Area

Popular Test Prep

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

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 : Solid Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #11 : Spheres

Example Question #14 : How To Find The Volume Of A Sphere

Example Question #12 : Spheres

Example Question #16 : How To Find The Volume Of A Sphere

Example Question #17 : How To Find The Volume Of A Sphere

Example Question #11 : Spheres

Example Question #13 : Spheres

Example Question #14 : Spheres

Example Question #21 : Spheres

Example Question #251 : Solid Geometry

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: