We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : Intermediate 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 #108 : Solid Geometry

Find the volume of a cylinder that has a radius of and a height of .

Possible Answers:

$2198\pi$

$2028\pi$

$2710\pi$

$1765\pi$

Correct answer:

$2028\pi$

Explanation:

Recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\text{Area of base}\times\text{height}$

Since the base of a cylinder is a circle, we can write the following equation:

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

Substitute in the given values to find the volume.

$\text{Volume of Cylinder}=\pi\times 13^2\times 144$

Solve.

$\text{Volume of Cylinder}=2028\pi$

Report an Error

Example Question #109 : Solid Geometry

Find the volume of a cylinder that has a radius of and a height of $\frac{1}{8}$ .

Possible Answers:

$\frac{1}{8}\pi$

$\frac{1}{4}\pi$

$\pi$

$\frac{1}{2}\pi$

Correct answer:

$\frac{1}{2}\pi$

Explanation:

Recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\text{Area of base}\times\text{height}$

Since the base of a cylinder is a circle, we can write the following equation:

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

Substitute in the given values to find the volume.

$\text{Volume of Cylinder}=\pi\times 2^2\times \frac{1}{8}$

Solve.

$\text{Volume of Cylinder}=\frac{1}{2}\pi$

Report an Error

Example Question #33 : Cylinders

Find the volume of a cylinder that has a radius of and a height of $\frac{1}{4}$ .

Possible Answers:

$81\pi$

$54\pi$

$324\pi$

$162\pi$

Correct answer:

$81\pi$

Explanation:

Recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\text{Area of base}\times\text{height}$

Since the base of a cylinder is a circle, we can write the following equation:

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

Substitute in the given values to find the volume.

$\text{Volume of Cylinder}=\pi\times 18^2\times \frac{1}{4}$

Solve.

$\text{Volume of Cylinder}=81\pi$

Report an Error

Example Question #111 : Solid Geometry

Find the volume of a cylinder that has a radius of $\frac{1}{5}$ and a height of $\frac{2}{3}$ .

Possible Answers:

$\frac{1}{25}\pi$

$\frac{1}{75}\pi$

$\frac{2}{75}\pi$

$\frac{4}{75}\pi$

Correct answer:

$\frac{2}{75}\pi$

Explanation:

Recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\text{Area of base}\times\text{height}$

Since the base of a cylinder is a circle, we can write the following equation:

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

Substitute in the given values to find the volume.

$\text{Volume of Cylinder}=\pi\times (\frac{1}{5})^2\times \frac{2}{3}$

Solve.

$\text{Volume of Cylinder}=\frac{2}{75}\pi$

Report an Error

Example Question #41 : Cylinders

A cylinder has a smaller cylinder cut out of its core as shown by the figure below.

Find the volume of the figure.

Possible Answers:

1425.32

1507.96

1607.55

1236.98

Correct answer:

1507.96

Explanation:

In order to find the volume of the figure, we will first need to find the volume of both cylinders.

Recall how to find the volume of the cylinder:

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

Now, use the given radius and height to find the volume of the larger cylinder.

$\text{Volume of Larger Cylinder}=\pi\times 7^2 \times 12=588\pi$

Next, use the given radius and height to find the volume of the smaller cylinder.

$\text{Volume of Smaller Cylinder}=\pi\times 3^2 \times 12=108\pi$

Subtract the volume of the smaller cylinder from the volume of the larger one to find the volume of the figure.

$\text{Volume of Figure}=588\pi-108\pi=480\pi=1507.96$

Make sure to round to places after the decimal.

Report an Error

Example Question #111 : Solid Geometry

Find the volume of the figure.

Possible Answers:

3369.61

3166.73

3209.58

3020.18

Correct answer:

3166.73

Explanation:

In order to find the volume of the figure, we will first need to find the volume of both cylinders.

Recall how to find the volume of the cylinder:

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

Now, use the given radius and height to find the volume of the larger cylinder.

$\text{Volume of Larger Cylinder}=\pi\times 10^2 \times 12=1200\pi$

Next, use the given radius and height to find the volume of the smaller cylinder.

$\text{Volume of Smaller Cylinder}=\pi\times 4^2 \times 12=192\pi$

Subtract the volume of the smaller cylinder from the volume of the larger one to find the volume of the figure.

$\text{Volume of Figure}=1200\pi-192\pi=1008\pi=3166.73$

Make sure to round to places after the decimal.

Report an Error

Example Question #112 : Solid Geometry

Find the volume of the figure.

Possible Answers:

29907.96

29632.23

30005.82

28800.64

Correct answer:

29907.96

Explanation:

In order to find the volume of the figure, we will first need to find the volume of both cylinders.

Recall how to find the volume of the cylinder:

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

Now, use the given radius and height to find the volume of the larger cylinder.

$\text{Volume of Larger Cylinder}=\pi\times 21^2 \times 35=15435\pi$

Next, use the given radius and height to find the volume of the smaller cylinder.

$\text{Volume of Smaller Cylinder}=\pi\times 13^2 \times 35=5915\pi$

Subtract the volume of the smaller cylinder from the volume of the larger one to find the volume of the figure.

$\text{Volume of Figure}=15435\pi-5915\pi=9520\pi=29907.96$

Make sure to round to places after the decimal.

Report an Error

Example Question #44 : Cylinders

Find the volume of the figure.

Possible Answers:

26551.22

21635.08

27159.63

26389.38

Correct answer:

26389.38

Explanation:

In order to find the volume of the figure, we will first need to find the volume of both cylinders.

Recall how to find the volume of the cylinder:

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

Now, use the given radius and height to find the volume of the larger cylinder.

$\text{Volume of Larger Cylinder}=\pi\times 20^2 \times 25=10000\pi$

Next, use the given radius and height to find the volume of the smaller cylinder.

$\text{Volume of Smaller Cylinder}=\pi\times 8^2 \times 25=1600\pi$

Subtract the volume of the smaller cylinder from the volume of the larger one to find the volume of the figure.

$\text{Volume of Figure}=10000\pi-1600\pi=8400\pi=26389.38$

Make sure to round to places after the decimal.

Report an Error

Example Question #45 : Cylinders

Find the volume of the figure.

Possible Answers:

15966.32

14844.03

15633.08

13222.07

Correct answer:

14844.03

Explanation:

In order to find the volume of the figure, we will first need to find the volume of both cylinders.

Recall how to find the volume of the cylinder:

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

Now, use the given radius and height to find the volume of the larger cylinder.

$\text{Volume of Larger Cylinder}=\pi\times 15^2 \times 25=5625\pi$

Next, use the given radius and height to find the volume of the smaller cylinder.

$\text{Volume of Smaller Cylinder}=\pi\times 6^2 \times 25=900\pi$

Subtract the volume of the smaller cylinder from the volume of the larger one to find the volume of the figure.

$\text{Volume of Figure}=5625\pi-900\pi=4725\pi=14844.03$

Make sure to round to places after the decimal.

Report an Error

Example Question #274 : New Sat

The figure below represents a cylinder with a smaller cylinder removed from its middle.

Find the volume of the figure.

Possible Answers:

1850.36

1865.32

1884.96

1896.77

Correct answer:

1884.96

Explanation:

In order to find the volume of the figure, we will first need to find the volume of both cylinders.

Recall how to find the volume of the cylinder:

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

Now, use the given radius and height to find the volume of the larger cylinder.

$\text{Volume of Larger Cylinder}=\pi\times 8^2 \times 10=640\pi$

Next, use the given radius and height to find the volume of the smaller cylinder.

$\text{Volume of Smaller Cylinder}=\pi\times 2^2 \times 10=40\pi$

Subtract the volume of the smaller cylinder from the volume of the larger one to find the volume of the figure.

$\text{Volume of Figure}=640\pi-40\pi=600\pi=1884.96$

Make sure to round to places after the decimal.

Report an Error

View Tutors

Juan
Certified Tutor

University of Central Florida, Bachelor of Science, Business, General.

View Tutors

Mihir
Certified Tutor

University of Massachusetts at Amherst, Bachelor of Science, Mechanical Engineering.

View Tutors

Ethan
Certified Tutor

Duke University, Bachelor, Molecular Bioscience: Cell and Molecular Biology.

All Intermediate Geometry Resources

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

Popular Subjects

Computer Science Tutors in San Diego, Math Tutors in Chicago, Math Tutors in Houston, Reading Tutors in Houston, LSAT Tutors in Houston, ISEE Tutors in Houston, ISEE Tutors in Seattle, ACT Tutors in Dallas Fort Worth, Biology Tutors in Philadelphia, SAT Tutors in San Diego

Popular Courses & Classes

SAT Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Chicago, GMAT Courses & Classes in Philadelphia, ISEE Courses & Classes in Los Angeles, ISEE Courses & Classes in Philadelphia, GRE Courses & Classes in Phoenix, GMAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Atlanta, ISEE Courses & Classes in Chicago, Spanish Courses & Classes in New York City

Popular Test Prep

ISEE Test Prep in Dallas Fort Worth, GRE Test Prep in Miami, GMAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Boston, SSAT Test Prep in Atlanta, ISEE Test Prep in Seattle, ISEE Test Prep in Washington DC, GRE Test Prep in Philadelphia, GRE Test Prep in Chicago, SSAT Test Prep in Phoenix

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 : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #108 : Solid Geometry

Example Question #109 : Solid Geometry

Example Question #33 : Cylinders

Example Question #111 : Solid Geometry

Example Question #41 : Cylinders

Example Question #111 : Solid Geometry

Example Question #112 : Solid Geometry

Example Question #44 : Cylinders

Example Question #45 : Cylinders

Example Question #274 : New Sat

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: