Call Now to Set Up Tutoring:

(888) 888-0446

Pre-Algebra : Volume of a Cone

Study concepts, example questions & explanations for Pre-Algebra

Create An Account

All Pre-Algebra Resources

11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Volume Of A Cone

The standard waffle cone at Cream Canyon Ice Cream Parlor has a diameter of 4 inches. If the height of the cone is 1.5 times the diameter, what is the volume of the cone?

Possible Answers:

$24\pi in.^{3}$

$12\pi in.^{3}$

$8\pi in.^{3}$

$48\pi in.^{3}$

$4\pi in.^{3}$

Correct answer:

$8\pi in.^{3}$

Explanation:

We must first recall the formula for the volume of a cone.

$V=\frac{1}{3}\pi r^{2}h$

where is the radius and is the height. The problem is that we are not provided with either the height or the radius. However, we are told that the height is 1.5 times the diameter. Since the diameter is 4 inches, we can calculate $1.5\cdot4=6$ . Thus the height of the cone is 6 inches. We must also recall that the radius of a circle (such as the top of an ice cream cone) is simply half the diameter. Therefore, if the diameter is 4 inches, the radius is 2 inches. We now have all of the essential ingredients for volume.

$V=\frac{1}{3}\pi (2)^{2}(6)= \frac{1}{3}\pi (24)=8\pi$

Since our measurements were all in inches, our volume will be in cubic inches. Therefore, the volume of our ice cream cone is $8\pi in.^3$ . Now all we need is a scoop or two of our favorite flavor.

Report an Error

Example Question #2 : Volume Of A Cone

Cone_1

Which of the following is the volume of the above cone?

Possible Answers:

$1,250 \pi$ cubic centimeters

$6,250 \pi$ cubic centimeters

$2,500 \pi$ cubic centimeters

$\frac{6,250\pi }{3}$ cubic centimeters

$\frac{2,500 \pi }{3}$ cubic centimeters

Correct answer:

$\frac{2,500 \pi }{3}$ cubic centimeters

Explanation:

The volume of a cone whose height is and whose base has radius is defined by the formula

$V = \frac{1}{3} \pi r^{2}h$ .

Set r = 10, h= 25 :

$V = \frac{1}{3} \pi \cdot 10 ^{2} \cdot 25$

$V = \frac{1}{3} \pi \cdot 100 \cdot 25$

$V = \frac{1}{3} \pi \cdot 2,500$

$V = \frac{2,500 \pi }{3}$ cubic centimeters.

Report an Error

Example Question #2 : Cones

The volume of a cone whose height is three times the radius of its base is one cubic yard. Give its radius in inches.

Possible Answers:

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

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

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

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

$\frac{ 12 \sqrt[3]{ \pi^{2} }}{ \pi}$

Correct answer:

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

Explanation:

The volume of a cone with base radius and height is

$V =\frac{1}{3} \pi r^{2}h$

The height is three times this, or . Therefore, the formula becomes

$V =\frac{1}{3} \pi r^{2} \cdot 3r$

$V = \pi r^{3}$

Set this volume equal to one and solve for :

$\pi r^{3} = 1$

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

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

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

This is the radius in yards; since the radius in inches is requested, multiply by 36.

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

Report an Error

Example Question #202 : Geometry

What is the volume of a cone with a radius of two and a height of three?

Possible Answers:

$18\pi$

$6\pi$

$24\pi$

$\pi$

$4\pi$

Correct answer:

$4\pi$

Explanation:

Write the formula to find the volume of the cone.

$V=\frac{1}{3}\pi r^2 h$

Substitute the radius and height.

$V=\frac{1}{3}\pi (2)^2 (3) = 4\pi$

Report an Error

Example Question #203 : Geometry

What is the volume of a cone with a radius of 5 and a height of 6?

Possible Answers:

$450\pi$

$50\pi$

$125\pi$

$150\pi$

$10\pi$

Correct answer:

$50\pi$

Explanation:

Write the formula to find the volume of a cone.

$V=\frac{1}{3} \pi r^2 h$

Substitute the dimensions and solve.

$V=\frac{1}{3} \pi (5)^2 (6) = \pi (5)^2 (2) = 50 \pi$

Report an Error

Example Question #204 : Geometry

Find the volume of a cone with a base area of and a height of .

Possible Answers:

$\frac{4}{9}\pi$

$2\pi$

$\frac{2}{3}$

$\frac{2}{3}\pi$

Correct answer:

$\frac{2}{3}$

Explanation:

The base of a cone has a circular cross section. Given the base area, there is no need to determine the radius.

Write the formula for the volume of a cone.

$V=\frac{1}{3} \pi r^2 h$

The $\pi r^2$ term represents the base area of the circle.

Substitute all the given values into the volume formula.

$V=\frac{1}{3} (\pi r^2) h = \frac{1}{3} (1) (2) = \frac{2}{3}$

Report an Error

Example Question #201 : Geometry

What is the volume of a cone with diameter of 2 and a height of 10?

Possible Answers:

$\frac{10}{3}\pi$

$\frac{40}{3}\pi$

$\frac{20}{3}\pi$

$\frac{200}{3}\pi$

$\frac{100}{3}\pi$

Correct answer:

$\frac{10}{3}\pi$

Explanation:

Write the formula for the volume of a cone.

$V=\frac{1}{3} \pi r^2h$

The radius is half the diameter.

Substitute the radius and the height.

$V=\frac{1}{3} \pi (1)^2(10) = \frac{10}{3}\pi$

Report an Error

Example Question #8 : Volume Of A Cone

Find the volume of a cone with a radius of and a height of .

Possible Answers:

$300\pi$

$\frac{101}{3}\pi$

$30\pi$

$303\pi$

$\frac{100}{3}\pi$

Correct answer:

$\frac{100}{3}\pi$

Explanation:

Write the volume formula for a cone.

$V=\frac{1}{3} \pi r^2 h$

Substitute the dimensions.

$V=\frac{1}{3} \pi (10)^2 (1) =\frac{100}{3}\pi$

Report an Error

Example Question #1 : Volume Of A Cone

Find the volume of the cone that has a radius of $\textup{3 feet}$ and a height of $\textup{2 feet}$ .

Possible Answers:

$18\pi\textup{ feet}^3$

$6\pi\textup{ feet}^3$

$6\pi\textup{ feet}^2$

$6\pi\textup{ feet}$

$18\pi\textup{ feet}^2$

Correct answer:

$6\pi\textup{ feet}^3$

Explanation:

Write the formula to find the volume of a cone.

$V=\frac{1}{3} \pi r^2 h$

$V=\frac{1}{3} \pi (3 \textup{ feet})^2 (2\textup{ feet}) =6\pi\textup{ feet}^3$

Report an Error

Example Question #211 : Geometry

Find the volume of a cone with a radius of and a height of .

Possible Answers:

$16\pi$

$117\pi$

$13\pi$

$39\pi$

$\frac{16}{3}\pi$

Correct answer:

$39\pi$

Explanation:

Write the formula to find the volume of the vone.

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

Substitute the dimensions into the formula.

$V_{cone}= \frac{1}{3} \pi (3)^2(13)$

Expand the terms.

$V_{cone}= \frac{1}{3} \pi (3\cdot3)(13) = \pi (3)(13)$

Multiply the integers for the volume.

$V_{cone} = 39\pi$

Report an Error

View Pre-Algebra Tutors

Oselen
Certified Tutor

UNIVERSITY OF BENIN, Bachelor of Science, Mechanical Engineering. University of Windsor, Master of Science, Mechanical Engine...

View Pre-Algebra Tutors

Karen
Certified Tutor

Oklahoma Panhandle State University, Bachelor of Science, Mathematics. Oklahoma Panhandle State University, Bachelor in Arts,...

View Pre-Algebra Tutors

Glauco
Certified Tutor

University of Mount Union, Bachelor of Science, Electrical Engineering.

All Pre-Algebra Resources

11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Spanish Tutors in Boston, LSAT Tutors in Houston, ISEE Tutors in Phoenix, Biology Tutors in Washington DC, French Tutors in Los Angeles, English Tutors in San Diego, ACT Tutors in New York City, ACT Tutors in Dallas Fort Worth, Statistics Tutors in Boston, ACT Tutors in Seattle

Popular Courses & Classes

GRE Courses & Classes in Los Angeles, ISEE Courses & Classes in Boston, ACT Courses & Classes in Miami, GRE Courses & Classes in San Diego, GMAT Courses & Classes in Washington DC, LSAT Courses & Classes in Miami, Spanish Courses & Classes in Atlanta, SSAT Courses & Classes in Phoenix, GRE Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Houston

Popular Test Prep

ISEE Test Prep in Miami, LSAT Test Prep in Boston, SAT Test Prep in Atlanta, SAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Los Angeles, SSAT Test Prep in Phoenix, MCAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Miami, SSAT Test Prep in Houston, ISEE 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

Pre-Algebra : Volume of a Cone

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #1 : Volume Of A Cone

Example Question #2 : Volume Of A Cone

Example Question #2 : Cones

Example Question #202 : Geometry

Example Question #203 : Geometry

Example Question #204 : Geometry

Example Question #201 : Geometry

Example Question #8 : Volume Of A Cone

Example Question #1 : Volume Of A Cone

Example Question #211 : Geometry

All Pre-Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: