Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : Cylinders

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 #31 : How To Find The Volume Of A Cylinder

Find the volume of the figure.

Possible Answers:

562020.12

485320.28

450000.12

494800.84

Correct answer:

494800.84

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.

$\text{Volume of Larger Cylinder}=\pi\times 50^2 \times 75=187500\pi$

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

$\text{Volume of Smaller Cylinder}=\pi\times 20^2 \times 75=30000\pi$

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

$\text{Volume of Figure}=187500\pi-30000\pi=157500\pi=494800.84$

Make sure to round to places after the decimal.

Report an Error

Example Question #52 : Cylinders

Find the volume of the figure.

Possible Answers:

16025.36

15833.63

14582.73

18552.20

Correct answer:

15833.63

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.

$\text{Volume of Larger Cylinder}=\pi\times 16^2 \times 20=5120\pi$

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

$\text{Volume of Smaller Cylinder}=\pi\times 2^2 \times 20=80\pi$

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

$\text{Volume of Figure}=5120\pi-80\pi=5040\pi=15833.63$

Make sure to round to places after the decimal.

Report an Error

Example Question #53 : Cylinders

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Find the volume of the figure.

Possible Answers:

4490.97

4242.68

4412.15

4509.20

Correct answer:

4490.97

Explanation:

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

From the figure, you should notice that the length of the prism is also the diameter of the half cylinder. Thus, half the length of the prism will also be the radius of the half cylinder. Also, notice that the width of the prism will be the height of the cylinder.

For the given cylinder then, find the radius.

$\text{radius}=\frac{\text{length}}{2}=\frac{12}{2}=6$

Then, recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi r^2 h$ , where is the radius and is the height.

Divide the volume by to find the volume of the half cylinder.

$\text{Volume of Half Cylinder}=\frac{\pi r^2 h}{2}$

$\text{Volume of Half Cylinder}=\frac{\pi (6)^2(20)}{2}=360\pi$

Next, recall how to find the volume of a rectangular prism.

$\text{Volume of Rectangular Prism}=\text{length}\times\text{width}\times\text{height}$

Plug in the given values to find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=(12)(20)(14)=3360$

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

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

$\text{Volume of Figure}=360\pi+3360=4490.97$

Remember to round to places after the decimal.

Report an Error

Example Question #54 : Cylinders

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Find the volume of the figure.

Possible Answers:

86.60

88.21

85.55

87.74

Correct answer:

87.74

Explanation:

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

For the given cylinder then, find the radius.

$\text{radius}=\frac{\text{length}}{2}=\frac{3}{2}$

Then, recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi r^2 h$ , where is the radius and is the height.

Divide the volume by to find the volume of the half cylinder.

$\text{Volume of Half Cylinder}=\frac{\pi r^2 h}{2}$

$\text{Volume of Half Cylinder}=\frac{\pi (\frac{3}{2})^2(7)}{2}=\frac{63}{8}\pi$

Next, recall how to find the volume of a rectangular prism.

$\text{Volume of Rectangular Prism}=\text{length}\times\text{width}\times\text{height}$

Plug in the given values to find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=(3)(7)(3)=63$

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

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

$\text{Volume of Figure}=\frac{63}{8}\pi+63=87.74$

Remember to round to places after the decimal.

Report an Error

Example Question #55 : Cylinders

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Find the volume of the figure.

Possible Answers:

2097.13

2014.56

2141.64

2088.69

Correct answer:

2097.13

Explanation:

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

For the given cylinder then, find the radius.

$\text{radius}=\frac{\text{length}}{2}=\frac{9}{2}$

Then, recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi r^2 h$ , where is the radius and is the height.

Divide the volume by to find the volume of the half cylinder.

$\text{Volume of Half Cylinder}=\frac{\pi r^2 h}{2}$

$\text{Volume of Half Cylinder}=\frac{\pi (\frac{9}{2})^2(15)}{2}=\frac{1215}{8}\pi$

Next, recall how to find the volume of a rectangular prism.

$\text{Volume of Rectangular Prism}=\text{length}\times\text{width}\times\text{height}$

Plug in the given values to find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=(9)(15)(12)=1620$

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

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

$\text{Volume of Figure}=\frac{1215}{8}\pi+1620=2097.13$

Remember to round to places after the decimal.

Report an Error

Example Question #56 : Cylinders

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Possible Answers:

2288.23

2678.92

2109.59

2389.55

Correct answer:

2288.23

Explanation:

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

For the given cylinder then, find the radius.

$\text{radius}=\frac{\text{length}}{2}=\frac{12}{2}=6$

Then, recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi r^2 h$ , where is the radius and is the height.

Divide the volume by to find the volume of the half cylinder.

$\text{Volume of Half Cylinder}=\frac{\pi r^2 h}{2}$

$\text{Volume of Half Cylinder}=\frac{\pi (6)^2(15)}{2}=270\pi$

Next, recall how to find the volume of a rectangular prism.

$\text{Volume of Rectangular Prism}=\text{length}\times\text{width}\times\text{height}$

Plug in the given values to find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=(12)(15)(8)=1440$

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

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

$\text{Volume of Figure}=270\pi+1440=2288.23$

Remember to round to places after the decimal.

Report an Error

Example Question #57 : Cylinders

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Possible Answers:

2241.20

2444.09

2590.15

2385.40

Correct answer:

2385.40

Explanation:

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

For the given cylinder then, find the radius.

$\text{radius}=\frac{\text{length}}{2}=\frac{10}{2}=5$

Then, recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi r^2 h$ , where is the radius and is the height.

Divide the volume by to find the volume of the half cylinder.

$\text{Volume of Half Cylinder}=\frac{\pi r^2 h}{2}$

$\text{Volume of Half Cylinder}=\frac{\pi (5)^2(20)}{2}=250\pi$

Next, recall how to find the volume of a rectangular prism.

$\text{Volume of Rectangular Prism}=\text{length}\times\text{width}\times\text{height}$

Plug in the given values to find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=(10)(20)(8)=1600$

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

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

$\text{Volume of Figure}=250\pi+1600=2385.40$

Remember to round to places after the decimal.

Report an Error

Example Question #58 : Cylinders

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Possible Answers:

4449.12

4443.22

4333.71

4902.56

Correct answer:

4443.22

Explanation:

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

For the given cylinder then, find the radius.

$\text{radius}=\frac{\text{length}}{2}=\frac{13}{2}$

Then, recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi r^2 h$ , where is the radius and is the height.

Divide the volume by to find the volume of the half cylinder.

$\text{Volume of Half Cylinder}=\frac{\pi r^2 h}{2}$

$\text{Volume of Half Cylinder}=\frac{\pi (\frac{13}{2})^2(17)}{2}=\frac{2873}{8}\pi$

Next, recall how to find the volume of a rectangular prism.

$\text{Volume of Rectangular Prism}=\text{length}\times\text{width}\times\text{height}$

Plug in the given values to find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=(13)(17)(15)=3315$

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

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

$\text{Volume of Figure}=\frac{2873}{8}\pi+3315=4443.22$

Remember to round to places after the decimal.

Report an Error

Example Question #59 : Cylinders

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Find the volume of the figure.

Possible Answers:

32.56

34.09

31.11

33.93

Correct answer:

33.93

Explanation:

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

For the given cylinder then, find the radius.

$\text{radius}=\frac{\text{length}}{2}=\frac{1}{2}$

Then, recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi r^2 h$ , where is the radius and is the height.

Divide the volume by to find the volume of the half cylinder.

$\text{Volume of Half Cylinder}=\frac{\pi r^2 h}{2}$

$\text{Volume of Half Cylinder}=\frac{\pi (\frac{1}{2})^2(10)}{2}=\frac{5}{4}\pi$

Next, recall how to find the volume of a rectangular prism.

$\text{Volume of Rectangular Prism}=\text{length}\times\text{width}\times\text{height}$

Plug in the given values to find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=(1)(10)(3)=30$

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

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

$\text{Volume of Figure}=\frac{5}{4}\pi+30=33.93$

Remember to round to places after the decimal.

Report an Error

Example Question #60 : Cylinders

Inscribed

The above diagram shows a sphere inscribed inside a cylinder.

The sphere has a volume of 100. Give the volume of the cylinder.

Possible Answers:

125

$116\frac{1}{6}$

$133\frac{1}{3}$

120

150

Correct answer:

150

Explanation:

Let be the radius of the sphere. Then the radius of the base of the cylinder is also , and the height of the cylinder is h = 2r .

The volume of the cylinder is

$V_{1} = \pi r^{2} h$ ,

which, after substituting, is

$V _{1} = \pi r^{2} (2r)$

$V_{1} =2 \cdot \pi r^{2}\cdot r$

$V_{1} =2 \pi r^{3}$

The volume of the sphere is

$V_{2} = \frac{4}{3} \pi r^{3}$

Therefore, the ratio of the former to the latter is

$\frac{V_{1} }{V_{2}}=\frac{ 2 \pi r^{3}}{\frac{4}{3}\pi r^{3}}$

$\frac{V_{1} }{V_{2}}=\frac{ 2 }{\frac{4}{3} } = 2 \cdot \frac{3}{4} = \frac{3}{2}$

and

$V_{1} = \frac{3}{2}V_{2}$

That is, the volume of the cylinder is $\frac{3}{2}$ times that of the sphere, so the volume of the cylinder is

$V_{1} = \frac{3}{2} \cdot 100 = 150$ .

Report an Error

View Tutors

Dante
Certified Tutor

New Jersey Institute of Technology, Bachelor of Science, Electrical Engineering. Stevens Institute of Technology, Master of S...

View Tutors

Andrew
Certified Tutor

University of Wisconsin-Stevens Point, Bachelor of Science, Mathematics. University of Wisconsin-Oshkosh, Master of Science, ...

View Tutors

Agnes
Certified Tutor

Cebu Normal University, Bachelor of Science, Mathematics.

All Intermediate Geometry Resources

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

Popular Subjects

French Tutors in Washington DC, Computer Science Tutors in Phoenix, Spanish Tutors in San Francisco-Bay Area, Chemistry Tutors in Philadelphia, Algebra Tutors in Washington DC, MCAT Tutors in Philadelphia, GRE Tutors in Boston, GMAT Tutors in Chicago, Physics Tutors in Miami, GRE Tutors in San Francisco-Bay Area

Popular Courses & Classes

Spanish Courses & Classes in Denver, ISEE Courses & Classes in Atlanta, Spanish Courses & Classes in New York City, Spanish Courses & Classes in Chicago, ISEE Courses & Classes in Philadelphia, GMAT Courses & Classes in Houston, SSAT Courses & Classes in Phoenix, GRE Courses & Classes in Philadelphia, ACT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in San Diego

Popular Test Prep

SAT Test Prep in Philadelphia, SAT Test Prep in Chicago, SSAT Test Prep in Los Angeles, SAT Test Prep in Dallas Fort Worth, SSAT Test Prep in Atlanta, GRE Test Prep in Houston, MCAT Test Prep in Boston, ISEE Test Prep in San Francisco-Bay Area, SSAT Test Prep in Boston, LSAT 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 : Cylinders

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

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

Example Question #52 : Cylinders

Example Question #53 : Cylinders

Example Question #54 : Cylinders

Example Question #55 : Cylinders

Example Question #56 : Cylinders

Example Question #57 : Cylinders

Example Question #58 : Cylinders

Example Question #59 : Cylinders

Example Question #60 : Cylinders

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: