Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Quantitative : How to find the radius of a sphere

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 #1 : How To Find The Radius Of A Sphere

The volume of a sphere is one cubic yard. Give its radius in inches.

Possible Answers:

$\frac{ 6\sqrt[3]{6 \pi^{2}} } {\pi} \textrm{ in}$

$\frac{ 18\sqrt{3 \pi } } {\pi} \textrm{ in}$

$\frac{ 18\sqrt[3]{6 \pi^{2}} } {\pi} \textrm{ in}$

$\frac{ \sqrt[3]{6 \pi^{2}} } {2\pi}\textrm{ in}$

$\frac{ \sqrt{3 \pi } } {2 \pi} \textrm{ in}$

Correct answer:

$\frac{ 18\sqrt[3]{6 \pi^{2}} } {\pi} \textrm{ in}$

Explanation:

The volume of a sphere with radius is

$V = \frac{4}{3} \pi r^{3}$ .

To find the radius in yards, we set V = 1 and solve for .

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

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

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

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

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

$r = \sqrt[3]{ \frac{3}{4\pi} } = \sqrt[3]{ \frac{3\cdot 2 \pi^{2}}{4\pi \cdot 2 \pi^{2}} }= \sqrt[3]{ \frac{6 \pi^{2}}{8 \pi^{3}} } = \frac{ \sqrt[3]{6 \pi^{2}} } {2\pi}$ yards.

Since the problem requests the radius in inches, multiply by 36:

$36 \times \frac{ \sqrt[3]{6 \pi^{2}} } {2\pi} = \frac{ 18\sqrt[3]{6 \pi^{2}} } {\pi}$

Report an Error

View Tutors

Jeromy
Certified Tutor

Washington State University, Bachelor of Science, Psychology. University of Washington-Seattle Campus, Master of Arts Teachin...

View Tutors

Robert
Certified Tutor

University of North Carolina at Chapel Hill, Bachelor in Arts, English. North Carolina Central University, Master of Arts, En...

View Tutors

Caroline
Certified Tutor

University of Florida, Bachelor of Science, Psychology.

All ISEE Upper Level Quantitative Resources

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

Popular Subjects

English Tutors in Phoenix, Spanish Tutors in Dallas Fort Worth, Reading Tutors in Houston, GMAT Tutors in New York City, Computer Science Tutors in Washington DC, MCAT Tutors in San Diego, Chemistry Tutors in Miami, GRE Tutors in San Diego, Calculus Tutors in Atlanta, English Tutors in San Francisco-Bay Area

Popular Courses & Classes

GMAT Courses & Classes in San Diego, GMAT Courses & Classes in Atlanta, ACT Courses & Classes in New York City, SAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Denver, MCAT Courses & Classes in San Diego, SSAT Courses & Classes in San Diego, ISEE Courses & Classes in Los Angeles, ACT Courses & Classes in Miami, ACT Courses & Classes in Atlanta

Popular Test Prep

GRE Test Prep in Philadelphia, GRE Test Prep in Denver, LSAT Test Prep in Philadelphia, ACT Test Prep in New York City, SSAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in San Francisco-Bay Area, SAT Test Prep in New York City, ISEE Test Prep in Los Angeles, GMAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Miami

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 : How to find the radius of a sphere

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #1 : How To Find The Radius Of A Sphere

All ISEE Upper Level Quantitative Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: