Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Quantitative : Cylinders

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

Create An Account

All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #347 : Geometry

What is the volume of a cylinder with a radius of 6 meters and a height of 11 meters? Use 3.14 for $\pi$ .

Note: The formula for the volume of a cylinder is:

$V=\pi r^2h$

Possible Answers:

396m^3

1432.23m^3

1243.44 m^3

207.24m^3

114.44m^3

Correct answer:

1243.44 m^3

Explanation:

To calculate the volume, you must plug into the formula given in the problem. When you plug in, it should look like this: V=(3.14)(6^2)(11) . Multiply all of these out and you get 1243.44m^3 . The units are cubed because volume is always cubed.

Report an Error

Example Question #1 : Cylinders

The volume of a cylinder whose height is twice the diameter of its base is one cubic yard. Give its radius in inches.

Possible Answers:

$\frac{ 9 \sqrt[3]{ 2 \pi^{2} } } {4 \pi } \textrm{ in}$

$\frac{ 18 \sqrt[3]{ 2 \pi^{2} } } {\pi } \textrm{ in}$

$\frac{ 9 \sqrt[3]{ 2 \pi^{2} } } {\pi } \textrm{ in}$

$\frac{ 9 \sqrt[3]{ 2 \pi^{2} } } {2 \pi } \textrm{ in}$

$\frac{ \sqrt[3]{ 2 \pi^{2} } } {2\pi } \textrm{ in}$

Correct answer:

$\frac{ 18 \sqrt[3]{ 2 \pi^{2} } } {\pi } \textrm{ in}$

Explanation:

The volume of a cylinder with base radius and height is

$V = \pi r^{2}h$

The diameter of this circle is ; its height is twice this, or . Therefore, the formula becomes

$V = \pi r^{2} \cdot 4r = 4\pi r^{3}$

Set this volume equal to one and solve for :

$4\pi r^{3} = 1$

$4\pi r^{3} \div 4\pi = 1 \div 4\pi$

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

$r =\sqrt[3]{ \frac{1}{4\pi }} =\frac{ \sqrt[3]{ 1 }} { \sqrt[3]{ 4\pi }} =\frac{ \sqrt[3]{ 1 } \cdot \sqrt[3]{ 2 \pi^{2} } } { \sqrt[3]{ 4\pi } \cdot \sqrt[3]{ 2 \pi^{2} }}=\frac{ \sqrt[3]{ 2 \pi^{2} } } {\sqrt[3]{ 8\pi^{3} }}=\frac{ \sqrt[3]{ 2 \pi^{2} } } {2\pi }$

This is the radius in yards; multiply by 36 to get the radius in inches.

$\frac{ \sqrt[3]{ 2 \pi^{2} } } {2\pi } \cdot 36 = \frac{ 18 \sqrt[3]{ 2 \pi^{2} } } {\pi }$

Report an Error

Example Question #2 : Cylinders

What is the height of a cylinder with a volume of $646.875\pi$ in^3 and a radius of 7.5 ?

Possible Answers:

28125.5

11.5

22.5

56250

86.25

Correct answer:

11.5

Explanation:

Recall that the equation of for the volume of a cylinder is:

$V = \pi * r^2 * h$

For our values this is:

$646.875\pi = \pi * 7.5^2 * h= \pi * 56.25 * h$

Solve for :

h = 11.5

Report an Error

Example Question #3 : Cylinders

What is the volume of a cylinder with a height of in. and a radius of in?

Possible Answers:

$180\pi$ in^3

$408\pi$ in^3

$720\pi$ in^3

$204\pi$ in^3

$300\pi$ in^3

Correct answer:

$720\pi$ in^3

Explanation:

This is a rather direct question. Recall that the equation of for the volume of a cylinder is:

$V = \pi * r^2 * h$

For our values this is:

$A = \pi * 12^2 * 5=720\pi$

This is the volume of the cylinder.

Report an Error

Example Question #5 : How To Find The Volume Of A Cylinder

What is the volume of a cylinder with a height of in. and a radius of 2.5 in?

Possible Answers:

$87.5\pi$ in^3

$82.5\pi$ in^3

$42.25\pi$ in^3

$70\pi$ in^3

$35\pi$ in^3

Correct answer:

$87.5\pi$ in^3

Explanation:

This is a rather direct question. Recall that the equation of for the volume of a cylinder is:

$V = \pi * r^2 * h$

For our values this is:

$A = \pi * 2.5^2 * 14=87.5\pi$

This is the volume of the cylinder.

Report an Error

Example Question #351 : Geometry

What is the radius of a cylinder with a volume of $562.5\pi$ in^3 and a height of ?

Possible Answers:

$56.25\pi$

56.25

$15\pi$

7.5

Correct answer:

7.5

Explanation:

Recall that the equation of for the volume of a cylinder is:

$V = \pi * r^2 * h$

For our values this is:

$562.5\pi = \pi * r^2 * 10$

Solve for :

56.25=r^2

Using a calculator to calculate $\sqrt{56.25}$ , you will see that r = 7.5

Report an Error

Example Question #1 : How To Find The Surface Area Of A Cylinder

What is the surface area of a cylinder of height in., with a radius of in?

Possible Answers:

$240\pi$ in^2

$136\pi$ in^2

$120\pi$ in^2

$152\pi$ in^2

$122\pi$ in^2

Correct answer:

$152\pi$ in^2

Explanation:

Recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. The equation for one base is:

$A = \pi * r^2$

For our problem, this is:

$\pi * 4^2 = \pi * 16$

You need to double this for the two bases:

$2 * 16 * \pi = 32 * \pi$

The area of the "outer face" is a little bit trickier, but it is not impossible. It is actually a rectangle that has the height of the cylinder and a width equal to the circumference of the base; therefore, it is:

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 4 * 15 = 120 * \pi$

Therefore, the total surface area is:

$32\pi + 120\pi = 152\pi$

Report an Error

Example Question #2 : Cylinders

What is the surface area of a cylinder having a base of radius in and a height of in?

Possible Answers:

$212\pi$ in^2

$308\pi$ in^2

$99\pi$ in^2

$363\pi$ in^2

$33\pi$ in^2

Correct answer:

$308\pi$ in^2

Explanation:

$A = \pi * r^2$

For our problem, this is:

$\pi * 11^2 = \pi * 121$

You need to double this for the two bases:

$2 * 121 * \pi = 242 * \pi$

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 11* 3 = 66 * \pi$

Therefore, the total surface area is:

$242 * \pi + 66 * \pi = 308\pi$

Report an Error

Example Question #3 : Cylinders

What is the surface area of a cylinder with a height of in. and a diameter of in?

Possible Answers:

$22\pi$ in^2

$57\pi$ in^2

$28\pi$ in^2

$36\pi$ in^2

$14\pi$ in^2

Correct answer:

$36\pi$ in^2

Explanation:

$A = \pi * r^2$

For our problem, this is:

$\pi * 2^2 = \pi * 4$

You need to double this for the two bases:

$2 * 4 * \pi = 8 * \pi$

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 2 * 7 = 28 * \pi$

Therefore, the total surface area is:

$28\pi + 8\pi = 36\pi$

Report an Error

Example Question #5 : Cylinders

The volume of a cylinder with height of is $275\pi$ in^3 . What is its surface area?

Possible Answers:

$66\pi$ in^2

$160\pi$ in^2

$82\pi$ in^2

$55\pi$ in^2

$135\pi$ in^2

Correct answer:

$160\pi$ in^2

Explanation:

To begin, we must solve for the radius of this cylinder. Recall that the equation of for the volume of a cylinder is:

$V = \pi * r^2 * h$

For our values this is:

$275\pi = \pi * r^2 * 11$

Solving for , we get:

r^2 = 25

Hence, r = 5

Now, recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. The equation for one base is:

$A = \pi * r^2$

For our problem, this is:

$\pi * 5^2 = \pi * 25$

You need to double this for the two bases:

$2 * 25 * \pi = 50 * \pi$

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 5 * 11 = 110 * \pi$

Therefore, the total surface area is:

$50\pi + 110\pi = 160\pi$

Report an Error

View Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

View Tutors

Gabby
Certified Tutor

University of Oregon, Bachelor in Arts, Journalism. University of Oregon, Current Grad Student, Communication, General.

View Tutors

Eva
Certified Tutor

Technicka Univerzita Liberec, Bachelor of Education, Education.

All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

MCAT Tutors in San Francisco-Bay Area, Calculus Tutors in Boston, ISEE Tutors in Houston, Physics Tutors in San Diego, Spanish Tutors in San Diego, SSAT Tutors in Denver, ISEE Tutors in San Diego, ISEE Tutors in Los Angeles, English Tutors in Dallas Fort Worth, Calculus Tutors in San Francisco-Bay Area

Popular Courses & Classes

MCAT Courses & Classes in Denver, LSAT Courses & Classes in Washington DC, MCAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Washington DC, GRE Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Houston, ISEE Courses & Classes in Denver, GMAT Courses & Classes in Atlanta, MCAT Courses & Classes in Miami, MCAT Courses & Classes in Los Angeles

Popular Test Prep

GMAT Test Prep in New York City, LSAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Philadelphia, GMAT Test Prep in Washington DC, LSAT Test Prep in Washington DC, SAT Test Prep in Los Angeles, ACT Test Prep in Houston, GRE Test Prep in Seattle, ISEE Test Prep in San Francisco-Bay Area, SSAT Test Prep in Houston

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

ISEE Upper Level Quantitative : Cylinders

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #347 : Geometry

Example Question #1 : Cylinders

Example Question #2 : Cylinders

Example Question #3 : Cylinders

Example Question #5 : How To Find The Volume Of A Cylinder

Example Question #351 : Geometry

Example Question #1 : How To Find The Surface Area Of A Cylinder

Example Question #2 : Cylinders

Example Question #3 : Cylinders

Example Question #5 : Cylinders

All ISEE Upper Level Quantitative Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: