Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : Solid 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 #62 : Spheres

Find the diameter of a sphere if the volume is $\pi^2$ .

Possible Answers:

$\sqrt[3]{\frac{3\pi}{4}}$

$2\sqrt\pi$

$\sqrt[3]{\frac{3}{4\pi}}$

$2\sqrt[3]{\frac{3\pi}{4}}$

$2\sqrt[3]{\frac{3}{4\pi}}$

Correct answer:

$2\sqrt[3]{\frac{3\pi}{4}}$

Explanation:

Write the volume for the sphere.

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

Substitute the volume and solve for the radius.

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

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

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

$r=\sqrt[3]{\frac{3}{4}\pi}$

Double the radius to find diameter.

$d=2\sqrt[3]{\frac{3}{4}\pi}$

Report an Error

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

Find the diameter of a sphere with the volume listed below.

$V=288\pi$

Possible Answers:

Correct answer:

Explanation:

In order to solve, we must the given volume into the volume formula for a sphere.

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

$288\pi =\frac{4}{3}\pi(r^{3})$

Divide both sides by pi.

$288 =\frac{4}{3}\(r^{3})$

Multiply both sides by 3.

$216 =(r^{3})$

Take the cube root of both sides to find the radius.

r=6

Double the radius to get the diameter, diameter is 12.

Report an Error

Example Question #7 : How To Find The Diameter Of A Sphere

Find the diameter of a sphere if it has a volume of $16\pi$ .

Possible Answers:

4.58

3.67

2.24

4.87

Correct answer:

4.58

Explanation:

Recall how to find the volume of a sphere:

$\text{Volume of Sphere}=\frac{4}{3}\pi r^3$ , where is the radius of the sphere.

Now, since the radius is half the diameter, the equation for the volume of a sphere can be rewritten as thus:

$\text{Volume of Sphere}=\frac{4}{3}\pi(\frac{d}{2})^3=\frac{1}{6}\pi d^3$ , where is the diameter of the sphere.

Rewrite the equation to solve for .

$d^3=\frac{6(\text{Volume of Sphere})}{\pi}$

$d=\sqrt[3]{\frac{6(\text{Volume of Sphere})}{\pi}}$

Now, plug in the volume of the sphere to find the diameter.

$d=\sqrt[3]{\frac{6(16\pi)}{\pi}}=4.58$

Report an Error

Example Question #8 : How To Find The Diameter Of A Sphere

Find the diameter of a sphere if it has a volume of $24\pi$ .

Possible Answers:

8.47

1.28

9.63

5.24

Correct answer:

5.24

Explanation:

Recall how to find the volume of a sphere:

$\text{Volume of Sphere}=\frac{4}{3}\pi r^3$ , where is the radius of the sphere.

Now, since the radius is half the diameter, the equation for the volume of a sphere can be rewritten as thus:

$\text{Volume of Sphere}=\frac{4}{3}\pi(\frac{d}{2})^3=\frac{1}{6}\pi d^3$ , where is the diameter of the sphere.

Rewrite the equation to solve for .

$d^3=\frac{6(\text{Volume of Sphere})}{\pi}$

$d=\sqrt[3]{\frac{6(\text{Volume of Sphere})}{\pi}}$

Now, plug in the volume of the sphere to find the diameter.

$d=\sqrt[3]{\frac{6(24\pi)}{\pi}}=5.24$

Report an Error

Example Question #9 : How To Find The Diameter Of A Sphere

Find the diameter of the sphere if it has a volume of $39\pi$ .

Possible Answers:

6.63

6.16

6.87

6.09

Correct answer:

6.16

Explanation:

Recall how to find the volume of a sphere:

$\text{Volume of Sphere}=\frac{4}{3}\pi r^3$ , where is the radius of the sphere.

Now, since the radius is half the diameter, the equation for the volume of a sphere can be rewritten as thus:

$\text{Volume of Sphere}=\frac{4}{3}\pi(\frac{d}{2})^3=\frac{1}{6}\pi d^3$ , where is the diameter of the sphere.

Rewrite the equation to solve for .

$d^3=\frac{6(\text{Volume of Sphere})}{\pi}$

$d=\sqrt[3]{\frac{6(\text{Volume of Sphere})}{\pi}}$

Now, plug in the volume of the sphere to find the diameter.

$d=\sqrt[3]{\frac{6(39\pi)}{\pi}}=6.16$

Report an Error

Example Question #10 : How To Find The Diameter Of A Sphere

Find the diameter of a sphere if it has a volume of 100 .

Possible Answers:

6.95

5.22

5.76

4.41

Correct answer:

5.76

Explanation:

Recall how to find the volume of a sphere:

$\text{Volume of Sphere}=\frac{4}{3}\pi r^3$ , where is the radius of the sphere.

Now, since the radius is half the diameter, the equation for the volume of a sphere can be rewritten as thus:

$\text{Volume of Sphere}=\frac{4}{3}\pi(\frac{d}{2})^3=\frac{1}{6}\pi d^3$ , where is the diameter of the sphere.

Rewrite the equation to solve for .

$d^3=\frac{6(\text{Volume of Sphere})}{\pi}$

$d=\sqrt[3]{\frac{6(\text{Volume of Sphere})}{\pi}}$

Now, plug in the volume of the sphere to find the diameter.

$d=\sqrt[3]{\frac{6(100)}{\pi}}=5.76$

Report an Error

Example Question #11 : How To Find The Diameter Of A Sphere

Find the diameter of a sphere if it has a volume of .

Possible Answers:

3.26

3.69

3.94

3.08

Correct answer:

3.94

Explanation:

Recall how to find the volume of a sphere:

$\text{Volume of Sphere}=\frac{4}{3}\pi r^3$ , where is the radius of the sphere.

Now, since the radius is half the diameter, the equation for the volume of a sphere can be rewritten as thus:

$\text{Volume of Sphere}=\frac{4}{3}\pi(\frac{d}{2})^3=\frac{1}{6}\pi d^3$ , where is the diameter of the sphere.

Rewrite the equation to solve for .

$d^3=\frac{6(\text{Volume of Sphere})}{\pi}$

$d=\sqrt[3]{\frac{6(\text{Volume of Sphere})}{\pi}}$

Now, plug in the volume of the sphere to find the diameter.

$d=\sqrt[3]{\frac{6(32)}{\pi}}=3.94$

Report an Error

Example Question #11 : How To Find The Diameter Of A Sphere

Find the diameter of the sphere if it has a volume of .

Possible Answers:

5.24

5.56

5.70

5.69

Correct answer:

5.56

Explanation:

Recall how to find the volume of a sphere:

$\text{Volume of Sphere}=\frac{4}{3}\pi r^3$ , where is the radius of the sphere.

Now, since the radius is half the diameter, the equation for the volume of a sphere can be rewritten as thus:

$\text{Volume of Sphere}=\frac{4}{3}\pi(\frac{d}{2})^3=\frac{1}{6}\pi d^3$ , where is the diameter of the sphere.

Rewrite the equation to solve for .

$d^3=\frac{6(\text{Volume of Sphere})}{\pi}$

$d=\sqrt[3]{\frac{6(\text{Volume of Sphere})}{\pi}}$

Now, plug in the volume of the sphere to find the diameter.

$d=\sqrt[3]{\frac{6(90)}{\pi}}=5.56$

Make sure to round to places after the decimal.

Report an Error

Example Question #12 : How To Find The Diameter Of A Sphere

Find the diameter of a sphere if it has a volume of $106\pi$ .

Possible Answers:

8.60

7.89

8.99

9.06

Correct answer:

8.60

Explanation:

Recall how to find the volume of a sphere:

$\text{Volume of Sphere}=\frac{4}{3}\pi r^3$ , where is the radius of the sphere.

Now, since the radius is half the diameter, the equation for the volume of a sphere can be rewritten as thus:

$\text{Volume of Sphere}=\frac{4}{3}\pi(\frac{d}{2})^3=\frac{1}{6}\pi d^3$ , where is the diameter of the sphere.

Rewrite the equation to solve for .

$d^3=\frac{6(\text{Volume of Sphere})}{\pi}$

$d=\sqrt[3]{\frac{6(\text{Volume of Sphere})}{\pi}}$

Now, plug in the volume of the sphere to find the diameter.

$d=\sqrt[3]{\frac{6(106\pi)}{\pi}}=8.60$

Make sure to round to places after the decimal.

Report an Error

Example Question #13 : How To Find The Diameter Of A Sphere

Find the diameter of a sphere that has a volume of $69\pi$ .

Possible Answers:

7.45

6.20

7.93

8.22

Correct answer:

7.45

Explanation:

Recall how to find the volume of a sphere:

$\text{Volume of Sphere}=\frac{4}{3}\pi r^3$ , where is the radius of the sphere.

Now, since the radius is half the diameter, the equation for the volume of a sphere can be rewritten as thus:

$\text{Volume of Sphere}=\frac{4}{3}\pi(\frac{d}{2})^3=\frac{1}{6}\pi d^3$ , where is the diameter of the sphere.

Rewrite the equation to solve for .

$d^3=\frac{6(\text{Volume of Sphere})}{\pi}$

$d=\sqrt[3]{\frac{6(\text{Volume of Sphere})}{\pi}}$

Now, plug in the volume of the sphere to find the diameter.

$d=\sqrt[3]{\frac{6(69\pi)}{\pi}}=7.45$

Make sure to round to places after the decimal.

Report an Error

View Tutors

Maria
Certified Tutor

Michigan State University, Bachelor of Education, Physiology. Central Michigan University, Master of Arts, Educational Admini...

View Tutors

Anjali
Certified Tutor

Delhi University, Bachelor of Science, Physics. Kumuan University, Master of Science, Physics.

View Tutors

Tesy
Certified Tutor

Texas State University-San Marcos, Master of Arts, Education.

All Intermediate Geometry Resources

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

Popular Subjects

GMAT Tutors in Boston, Calculus Tutors in Houston, Spanish Tutors in Miami, ACT Tutors in Houston, Physics Tutors in San Diego, Algebra Tutors in Washington DC, English Tutors in Chicago, Calculus Tutors in Washington DC, Reading Tutors in Miami, Reading Tutors in Phoenix

Popular Courses & Classes

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

Popular Test Prep

GRE Test Prep in Phoenix, ISEE Test Prep in Washington DC, MCAT Test Prep in Denver, GRE Test Prep in Los Angeles, GRE Test Prep in New York City, ACT Test Prep in Washington DC, GRE Test Prep in Philadelphia, LSAT Test Prep in Dallas Fort Worth, GMAT Test Prep in Denver, ACT 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

Intermediate Geometry : Solid Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #62 : Spheres

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

Example Question #7 : How To Find The Diameter Of A Sphere

Example Question #8 : How To Find The Diameter Of A Sphere

Example Question #9 : How To Find The Diameter Of A Sphere

Example Question #10 : How To Find The Diameter Of A Sphere

Example Question #11 : How To Find The Diameter Of A Sphere

Example Question #11 : How To Find The Diameter Of A Sphere

Example Question #12 : How To Find The Diameter Of A Sphere

Example Question #13 : How To Find The Diameter Of A Sphere

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: