We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

GED Math : 3-Dimensional Geometry

Study concepts, example questions & explanations for GED Math

Create An Account

All GED Math Resources

4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : 3 Dimensional Geometry

What is the volume of a sphere with a radius of $\frac{3}{2}\pi$ ?

Possible Answers:

$\frac{9}{2}\pi ^4$

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

$9\pi ^3$

$\frac{9}{8}\pi ^6$

$\frac{9}{2}\pi ^3$

Correct answer:

$\frac{9}{2}\pi ^4$

Explanation:

Write the formula for the volume of a sphere.

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

Substitute the radius into this equation.

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

The answer is: $\frac{9}{2}\pi ^4$

Report an Error

Example Question #12 : 3 Dimensional Geometry

Determine the volume of a sphere in feet, if the diameter of the sphere is 6 inches.

Possible Answers:

$\frac{1}{96}\pi \textup{ ft}^3$

$\frac{1}{124}\pi \textup{ ft}^3$

$288\pi \textup{ ft}^3$

$\frac{1}{24} \pi\textup{ ft}^3$

$\frac{1}{48}\pi \textup{ ft}^3$

Correct answer:

$\frac{1}{48}\pi \textup{ ft}^3$

Explanation:

Write the formula for the volume of a sphere.

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

We will need to convert the diameter in terms of feet. There are 12 inches to a foot.

$6 \textup{ in} (\frac{1 \textup{ ft}}{12 \textup{ in}}) = \frac{1}{2} \textup{ ft}$

The radius is half the diameter. Multiply this value by one-half to obtain the radius.

$\frac{1}{2} \textup{ ft} \cdot \frac{1}{2} = \frac{1}{4} \textup{ ft}$

Substitute the radius in the formula.

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

The answer is: $\frac{1}{48}\pi \textup{ ft}^3$

Report an Error

Example Question #13 : 3 Dimensional Geometry

Let $\pi = 3.14$ .

If a sphere has a radius of 3cm, find the volume.

Possible Answers:

$25.12\text{cm}^3$

$113.04\text{cm}^3$

$28.26\text{cm}^3$

$37.68\text{cm}^3$

$84.78\text{cm}^3$

Correct answer:

$113.04\text{cm}^3$

Explanation:

To find the volume of a sphere, we will use the following formula:

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

where r is the radius of the sphere.

Now, we know $\pi = 3.14$ . We know the radius of the sphere is 3cm. So, we can substitute. We get

$V = \frac{4}{3} \cdot 3.14 \cdot (3\text{cm})^3$

$V = \frac{4}{3} \cdot 3.14 \cdot 27\text{cm}^3$

$V = \frac{4}{3} \cdot 27\text{cm}^3 \cdot 3.14$

Now, the 3 and the 27 can both be divided by 3. So, we get

$V = \frac{4}{1} \cdot 9\text{cm}^3 \cdot 3.14$

$V = 4 \cdot 9\text{cm}^3 \cdot 3.14$

$V = 36\text{cm}^3 \cdot 3.14$

$V = 113.04\text{cm}^3$

Report an Error

Example Question #561 : Geometry And Graphs

Find the volume of a sphere with a radius of $\frac{3}{4}\pi$ .

Possible Answers:

$\frac{9}{16} \pi ^4$

$\frac{9}{16}\pi$

$\pi ^3$

$\frac{9}{4} \pi ^3$

$\pi^4$

Correct answer:

$\frac{9}{16} \pi ^4$

Explanation:

Write the formula for the volume of a sphere.

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

Substitute the radius into the equation.

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

The answer is: $\frac{9}{16} \pi ^4$

Report an Error

Example Question #11 : 3 Dimensional Geometry

Determine the volume of a sphere with a radius of 6.

Possible Answers:

$72\pi$

$288\pi$

$144\pi$

$48\pi$

$324\pi$

Correct answer:

$288\pi$

Explanation:

Write the formula for the volume of a sphere.

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

Substitute the radius.

$V= \frac{4}{3}\pi (6)^3 = \frac{4}{3}\pi (6) (6) (6) = 288\pi$

The answer is: $288\pi$

Report an Error

Example Question #13 : Volume Of A Sphere

Find the volume of a sphere with a radius of 6cm.

Possible Answers:

$216\pi \text{ cm}^3$

$72\pi \text{ cm}^3$

$648\pi \text{ cm}^3$

$864\pi \text{ cm}^3$

$288\pi \text{ cm}^3$

Correct answer:

$288\pi \text{ cm}^3$

Explanation:

To find the volume of a sphere, we will use the following formula:

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

where r is the radius of the sphere.

Now, we know the radius of the sphere is 6cm. So, we can substitute. We get

$V = \frac{4}{3} \cdot \pi \cdot (6\text{cm})^3$

$V = \frac{4}{3} \cdot \pi \cdot 216\text{cm}^3$

Now, the 3 and the 216 can both be divided by 3. So, we get

$V= \frac{4}{1} \cdot \pi \cdot 72\text{cm}^3$

$V= 4 \cdot \pi \cdot 72\text{cm}^3$

$V = 4 \cdot 72\text{cm}^3 \cdot \pi$

$V = 288\text{cm}^3 \cdot \pi$

$V = 288\pi \text{ cm}^3$

Report an Error

Example Question #16 : 3 Dimensional Geometry

Find the volume of a sphere with a surface area of $4\pi$ .

Possible Answers:

$\frac{256}{3}\pi$

$\frac{4}{3} \pi$

$\pi$

$\frac{1}{3}\pi$

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

Correct answer:

$\frac{4}{3} \pi$

Explanation:

Write the formulas for the surface area and volume of a sphere.

$A = 4\pi r^2$

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

Substitute the surface area into the first formula and solve for the radius.

$4\pi = 4\pi r^2$

Divide by $4\pi$ on both sides.

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

1=r^2

Square root both sides.

r=1

Substitute the radius into the volume formula.

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

The answer is: $\frac{4}{3} \pi$

Report an Error

Example Question #563 : Geometry And Graphs

Find the volume of a sphere with a radius of $\pi ^6$ .

Possible Answers:

$\frac{4}{3}\pi ^{19}$

$4\pi^{10}$

$\frac{16}{3}\pi ^{10}$

$\frac{4}{3}\pi ^{10}$

$\frac{16}{3}\pi ^{19}$

Correct answer:

$\frac{4}{3}\pi ^{19}$

Explanation:

Write the formula for the volume of a sphere.

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

Substitute the radius.

$V=\frac{4}{3}\pi (\pi ^6)^3= \frac{4}{3}\pi (\pi ^6) (\pi ^6) (\pi ^6)$

The answer is: $\frac{4}{3}\pi ^{19}$

Report an Error

Example Question #571 : Geometry And Graphs

You are 3D printing a ball which will be an integral piece to the project you are creating. If you need the ball to have a radius of 12cm, what volume of material will be required?

Possible Answers:

7234.56 cm^3

1728 cm^3

2304 cm^3

$144\pi cm^3$

Correct answer:

7234.56 cm^3

Explanation:

You are 3D printing a ball which will be an integral piece to the project you are creating. If you need the ball to have a radius of 12cm, what volume of material will be required?

We are asked to find the volume of a sphere, to do so, we should use the formula for volume of a sphere.

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

So, let's plug in our radius and solve:

$V_{sphere}=\frac{4}{3} \pi (12cm)^3=\frac{4}{3} \pi 1728cm^3=7234.56 cm^3$

So our answer is:

7234.56 cm^3

Report an Error

Example Question #12 : 3 Dimensional Geometry

You are given a spherical floating speaker for your birthday. If the speaker has a radius of 5 inches, what is its volume?

Possible Answers:

523.56in^3

500in^3

166.67in^3

125in^3

Correct answer:

523.56in^3

Explanation:

You are given a spherical floating speaker for your birthday. If the speaker has a radius of 5 inches, what is its volume?

We need to find the volume of a sphere. To do so, we need the following formula:

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

We know r is 5, so just plug and simplify

$V=\frac{4}{3}\pi (5in)^3\approx 523.56in^3$

Report an Error

View Tutors

Kaylee
Certified Tutor

Brigham Young University, Bachelor, MFA - Animation.

View Tutors

Angela
Certified Tutor

North Georgia College State University, Bachelor of Science, Special Education. North Georgia College State University, Mas...

View Tutors

Dereika
Certified Tutor

Southern University and A & M College, Bachelor of Science, Accounting. Grand Canyon University, Master of Science, Accounting.

All GED Math Resources

4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in New York City, Chemistry Tutors in Denver, ISEE Tutors in New York City, SAT Tutors in Boston, LSAT Tutors in New York City, French Tutors in San Francisco-Bay Area, SAT Tutors in Denver, Reading Tutors in San Francisco-Bay Area, Math Tutors in Boston, Spanish Tutors in San Francisco-Bay Area

Popular Courses & Classes

SAT Courses & Classes in Houston, MCAT Courses & Classes in Philadelphia, GRE Courses & Classes in Phoenix, MCAT Courses & Classes in Seattle, SAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in New York City, ACT Courses & Classes in Philadelphia, MCAT Courses & Classes in Phoenix, Spanish Courses & Classes in Seattle, GMAT Courses & Classes in Seattle

Popular Test Prep

ACT Test Prep in Los Angeles, ISEE Test Prep in New York City, GRE Test Prep in Boston, ISEE Test Prep in Phoenix, ISEE Test Prep in Atlanta, SSAT Test Prep in San Diego, LSAT Test Prep in Boston, GRE Test Prep in Los Angeles, GRE Test Prep in Washington DC, MCAT Test Prep in Seattle

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

GED Math : 3-Dimensional Geometry

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #11 : 3 Dimensional Geometry

Example Question #12 : 3 Dimensional Geometry

Example Question #13 : 3 Dimensional Geometry

Example Question #561 : Geometry And Graphs

Example Question #11 : 3 Dimensional Geometry

Example Question #13 : Volume Of A Sphere

Example Question #16 : 3 Dimensional Geometry

Example Question #563 : Geometry And Graphs

Example Question #571 : Geometry And Graphs

Example Question #12 : 3 Dimensional Geometry

All GED Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: