Call Now to Set Up Tutoring:

(888) 888-0446

GED Math : GED Math

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 #41 : 3 Dimensional Geometry

Prism

One cubic centimeter of pure iron is about $7.9 \textup{ grams}$ in mass.

Using this figure, what is the mass, in kilograms, of the above iron bar?

Possible Answers:

$568.8 \textup{ kg}$

$56.8 8 \textup{ kg}$

$114\textup{ kg}$

$11.4 \textup{ kg}$

Correct answer:

$568.8 \textup{ kg}$

Explanation:

First, convert the dimensions of the prism to centimeters. One meter is equal to 100 centimeters, so multiply by this conversion factor:

$0.8 \textup{ m } \times 100 \textup{ cm /m} = 80 \textup{ cm}$

$0.3 \textup{ m } \times 100 \textup{ cm /m} =30 \textup{ cm}$

The dimensions of the prism are 80 centimeters by 30 centimeters by centimeters; multiply these dimensions to find the volume:

$V = 80 \textup{ cm} \times 30 \textup{ cm} \times 30 \textup{ cm}$

$= 72,000 \textup{ cm}^{3}$

Using the given mass of 7.9 grams per cubic centimeter, multiply:

$M = 72,000 \textup{ cm}^{3} \times 7.9 \textup{ g / cm}^{3} = 568,800 \textup{ g}$

One kilogram is equal to 1,000 grams, so divide by this conversion factor:

$M = 568,800 \textup{ g} \div 1,000 \textup{ g / kg} = 568.8 \textup{ kg}$ ,

the correct mass of the prism.

Report an Error

Example Question #11 : Volume Of A Rectangular Solid

Find the volume of a rectangular prism with the following dimensions: 6 ft by 12 ft by 4 ft.

Possible Answers:

198 ft^3

208 ft^3

288 ft^3

148 ft^3

Correct answer:

288 ft^3

Explanation:

Find the volume of a rectangular prism with the following dimensions: 6 ft by 12 ft by 4 ft.

To find the volume of a rectangular prism, simply multiply the length by the width by the height.

V=l*w*h

So, plug in and multiply to get:

V=6ft*4ft*12ft=24ft^2*12ft=288ft^3

So, our answer is:

288 ft^3

Coincidentally the same as our surface area

Report an Error

Example Question #12 : Volume Of A Rectangular Solid

What is the volume of a box with length of 3 feet, width of 5 feet, and height of 2 feet?

Possible Answers:

12 feet squared

7 feet squared

15 feet squared

10 feet squared

30 feet squared

Correct answer:

30 feet squared

Explanation:

The equation for the volume of a rectangular prism is

$V=l\cdot w \cdot h$

So we simply input our dimensions

$V=5\cdot2\cdot3=30$

Report an Error

Example Question #1 : Volume Of A Cylinder

One cubic foot is equal to (about) 7.5 gallons.

A circular swimming pool has diameter 60 feet and depth five feet throughout. Using the above conversion factor, how many gallons of water does it hold?

Use 3.14 for $\pi$ .

Possible Answers:

$24,320\textrm{ gal}$

$7,065 \textrm{ gal }$

$105,975\textrm{ gal }$

$211,950\textrm{ gal }$

Correct answer:

$105,975\textrm{ gal }$

Explanation:

The pool can be seen as a cylinder with depth (or height) 5 feet, and a base with diameter 60 feet - and radius half this, or 30 feet. The capacity of the pool is the volume of this cylinder, which is

$V = \pi r ^{2} h = 3.14 \times 30^{2} \times 5 = 14,130$ cubic feet.

One cubic foot is equal to 7.5 gallons, so multiply:

$14,130 \times 7.5 = 105,975$ gallons

Report an Error

Example Question #2 : Volume Of A Cylinder

A cylindrical bucket is one foot high and one foot in diameter. It is filled with water, which is then emptied into an empty barrel three feet high and two feet in diameter. What percent of the barrel has been filled?

Possible Answers:

$12 \%$

$18 \%$

$16\frac{2}{3} \%$

$8 \frac{1}{3} \%$

Correct answer:

$8 \frac{1}{3} \%$

Explanation:

The volume of a cylinder is

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

The bucket has height h = 1 and diameter 1, and,subsequently, radius $r = \frac{1}{2}$ ; its volume is

$V = \pi r^{2}h = \pi \cdot \left (\frac{1}{2} \right ) ^{2} \cdot 1 =\frac{1}{4} \pi$ cubic feet

The barrel has height h = 3 and diameter 2,and, subsequently, radius r = 1 ; its volume is

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

The volume of the bucket is

$\frac{\frac{1}{4}\pi}{3 \pi} \times 100 \%$

$=\left ( \frac{1}{4}\pi \div 3 \pi \right )\times 100 \%$

$=\left ( \frac{\pi}{4}\times \frac{1}{3 \pi} \right )\times 100\%$

$= \frac{1}{12} \times 100\% = 8 \frac{1}{3} \%$

Report an Error

Example Question #1 : Volume Of A Cylinder

A water tank takes the shape of a closed cylinder whose exterior has height 30 feet and a base with radius 10 feet; the tank is three inches thick throughout. To the nearest hundred, how many cubic feet of water does the tank hold?

You may use 3.14 for $\pi$ .

Possible Answers:

$8,400 \textrm{ ft}^{3}$

$9,400 \textrm{ ft}^{3}$

$9,000 \textrm{ ft}^{3}$

$8,800 \textrm{ ft}^{3}$

Correct answer:

$8,800 \textrm{ ft}^{3}$

Explanation:

Three inches is equal to 0.25 feet, so the height of the interior of the tank is

$30 - 2 \times 0.25 = 30 - 0.5 = 29.5$ inches.

The radius of the interior of the tank is

10 - 0.25 = 9.75 inches.

The amount of water the tank holds is the volume of the interior of the tank, which is

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

$V \approx 3.14 \cdot 9.75 ^{2} \cdot 29.5$

$V \approx 3.14 \cdot 9.75 ^{2} \cdot 29.5 \approx 8,806$ cubic feet.

This rounds to 8,800 cubic feet.

Report an Error

Example Question #1 : Volume Of A Cylinder

Barrel

The above diagram is one of a cylindrical tub. The company wants to make a cylindrical tub with three times the volume, but whose base is only twice the radius. How high should this new tub be?

Possible Answers:

$60\textrm{ in}$

$30\textrm{ in}$

$53 \frac{1}{3}\textrm{ in}$

$26 \frac{2}{3}\textrm{ in}$

Correct answer:

$30\textrm{ in}$

Explanation:

The volume of the given tub can be expressed using the following formula, setting r = 25 and h= 40 :

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

$V = \pi \cdot 25^{2} \cdot 40$

$V = 25,000 \pi$ cubic inches.

The new tub should have three times this volume, or

$V = 25,000 \pi \cdot 3 = 75,000 \pi$ cubic inches.

The radius is to be twice that of the above tub, which will be

$r = 25 \cdot 2 = 50$ inches.

The height can therefore be calculated as follows:

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

$\pi \cdot 50^{2} \cdot h = 75,000 \pi$

$2,500 \pi h = 75,000 \pi$

$h = \frac{75,000 \pi}{2,500 \pi} = 30$ inches

Report an Error

Example Question #3 : Volume Of A Cylinder

Barrel

Refer to the cylinder in the above diagram.

A cone has twice the volume and twice the height of the cylinder. What is the radius of the base of the cone (nearest tenth of an inch, if applicable)?

Possible Answers:

$43.3 \textup{ in}$

$50\textup{ in}$

$35.4\textup{ in}$

$75 \textup{ in}$

Correct answer:

$43.3 \textup{ in}$

Explanation:

The formula for the volume of the cylinder is

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

where and are the base radius and height of the cylinder.

Set r = 25, h = 40 in the formula to find the volume of the cylinder:

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

$v = \pi \cdot 25^{2} \cdot 40 = \pi \cdot 625 \cdot 40 = 25,000 \pi$

The cylinder will have volume twice this, or $50,000 \pi$ , and height twice the height of the cylinder, which is 80 inches.

The formula for the volume of the cone is

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

so we set $V = 50,000 \pi$ and h = 80 and solve for :

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

$\frac{ \pi r^{2} \cdot 80}{3} = 50,000 \pi$

$\frac{ \pi r^{2} \cdot 80}{3} \cdot \frac{3}{80 \pi} = 50,000 \pi \cdot \frac{3}{80 \pi}$

$r^{2} = \frac{150,000 \pi}{80 \pi} = 1,875$

$r = \sqrt{1,875} \approx 43.3$ inches.

Report an Error

Example Question #1 : Volume Of A Cylinder

Barrel

The above diagram is one of a cylindrical tub. The tub is holding water at 40% capacity. To the nearest cubic foot, how much more water can it hold?

Possible Answers:

$75 \textup{ ft}^{3}$

$45 \textup{ ft}^{3}$

$27 \textup{ ft}^{3}$

$18 \textup{ ft}^{3}$

Correct answer:

$27 \textup{ ft}^{3}$

Explanation:

The volume of the cylinder can be calculated using the following formula, setting r = 25 and h= 40 :

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

$V \approx 3.14 \cdot 25^{2} \cdot 40 \approx 78,539.8$ cubic inches.

The tub is 40% full, so it is 60% empty; it can hold

$78,539.8 \times 0.60 \approx 47,123.9$ more cubic inches of water.

The problem asks for the number of cubic feet, so divide by the cube of 12, or 1,728:

$47,123.9 \div 1,728 \approx 27.2$

The correct response is 27 cubic feet.

Report an Error

Example Question #3 : Volume Of A Cylinder

A circular swimming pool has diameter 40 feet and depth six feet throughout. How many cubic feet of water does it hold? (nearest cubic foot)

Use 3.14 as the value of $\pi$ .

Possible Answers:

$15,072 \textrm{ ft}^{3}$

$7,536 \textrm{ ft}^{3}$

$754 \textrm{ ft}^{3}$

$1,507 \textrm{ ft}^{3}$

Correct answer:

$7,536 \textrm{ ft}^{3}$

Explanation:

The pool can be seen as a cylinder with depth (or height) six feet and a base with diameter 40 feet - and radius half this, or 20 feet. The capacity of the pool is the volume of this cylinder, which is

$V = \pi r ^{2} h \approx 3.14 \times 20^{2} \times 6 = 7,536$ cubic feet.

Report an Error

View Tutors

Edmund
Certified Tutor

University of Ghana, Bachelor of Science, Statistics. university of Ghana, Master of Philosophy, Statistics.

View Tutors

Prince
Certified Tutor

Federal University of Technology, Owerri, Bachelor, Engineering. Evergreen College, Master's/Graduate, Business .

View Tutors

Bailey
Certified Tutor

University of Arizona, Bachelor of Science, Biochemistry.

All GED Math Resources

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

Popular Subjects

English Tutors in New York City, Algebra Tutors in Dallas Fort Worth, Chemistry Tutors in San Francisco-Bay Area, Computer Science Tutors in Boston, SAT Tutors in Boston, LSAT Tutors in Denver, Chemistry Tutors in Boston, SAT Tutors in San Francisco-Bay Area, Calculus Tutors in Chicago, ACT Tutors in Miami

Popular Courses & Classes

SSAT Courses & Classes in New York City, GRE Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Denver, ACT Courses & Classes in Washington DC, SSAT Courses & Classes in Houston, MCAT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Los Angeles, SSAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Philadelphia

Popular Test Prep

ISEE Test Prep in Philadelphia, SAT Test Prep in Boston, ISEE Test Prep in Dallas Fort Worth, SAT Test Prep in San Diego, MCAT Test Prep in Washington DC, GRE Test Prep in San Diego, GMAT Test Prep in Dallas Fort Worth, SAT Test Prep in Washington DC, GRE Test Prep in Dallas Fort Worth, MCAT Test Prep in Chicago

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 : GED Math

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #41 : 3 Dimensional Geometry

Example Question #11 : Volume Of A Rectangular Solid

Example Question #12 : Volume Of A Rectangular Solid

Example Question #1 : Volume Of A Cylinder

Example Question #2 : Volume Of A Cylinder

Example Question #1 : Volume Of A Cylinder

Example Question #1 : Volume Of A Cylinder

Example Question #3 : Volume Of A Cylinder

Example Question #1 : Volume Of A Cylinder

Example Question #3 : Volume Of A Cylinder

All GED Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: