GMAT Math : Cubes

Study concepts, example questions & explanations for GMAT Math

Create An Account

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 Next →

Example Question #831 : Gmat Quantitative Reasoning

A sphere with volume $36 \pi$ is inscribed inside a cube. Give the volume of the cube.

Possible Answers:

216

$72\sqrt{3}$

$36 \sqrt{6}$

$27 \sqrt{3}$

Correct answer:

216

Explanation:

The sidelength of the cube is the diameter of the inscribed sphere, which is twice that sphere's radius. The sphere has volume $36 \pi$ , so the radius is calculated as follows:

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

$\frac{4}{3} \pi r^{3} = 36 \pi$

$r^{3} = 36\pi \div \left (\frac{4}{3} \pi \right )$

$r^{3} = 27$

$r = \sqrt[3]{27} = 3$

The diameter of the sphere - and the sidelength of the cube - is twice this, or 6. Cube this sidelength to get the volume of the cube:

$V = 6^{3} = 216$

Report an Error

Example Question #832 : Gmat Quantitative Reasoning

The distance from one vertex of a cube to its opposite vertex is twelve feet. Give the volume of the cube.

Possible Answers:

$32\sqrt{2} \textup{ yd}^{3}$

$\frac{64 \sqrt{2}}{6} \textup{ yd}^{3}$

$\frac{64 \sqrt{3}}{9} \textup{ yd}^{3}$

$\frac{64 }{9} \textup{ yd}^{3}$

$32\sqrt{3} \textup{ yd}^{3}$

Correct answer:

$\frac{64 \sqrt{3}}{9} \textup{ yd}^{3}$

Explanation:

Since we are looking at yards, we will look at twelve feet as four yards.

Let be the length of one edge of the cube. By the three-dimensional extension of the Pythagorean Theorem,

$s^{2}+s^{2}+s^{2}=4^{2}$

$3s^{2}=16$

$s^{2}= \frac{16}{3}$

$s^{2}= \sqrt{\frac{16}{3}} = \frac{\sqrt{16}}{\sqrt{3}} = \frac{4}{\sqrt{3}}$ yards.

Cube this sidelength to get the volume:

$s^{3}= \left ( \frac{4}{\sqrt{3}} \right )^{3} = \frac{4^{3}}{(\sqrt{3})^{3}} = \frac{64 }{3\sqrt{3} }= \frac{64 \cdot \sqrt{3}}{3\sqrt{3}\cdot \sqrt{3} } = \frac{64 \sqrt{3}}{9}$ cubic yards.

Report an Error

Example Question #833 : Gmat Quantitative Reasoning

An aquarium is shaped like a perfect cube; the area of each glass face is 6.25 square meters. If it is filled to the recommended $80\%$ capacity, then how much water will it contain?

Note: cubic meter = 1,000 liters.

Possible Answers:

$12,500\textup{ L}$

The correct answer is not given among the other choices.

$8,000\textup{ L}$

$10,000\textup{ L}$

$15,625\textup{ L}$

Correct answer:

$12,500\textup{ L}$

Explanation:

A perfect cube has square faces; if a face has area 6.25 square meters, then each side of each face measures the square root of this, or 2.5 meters. The volume of the tank is the cube of this, or

$2.5^{3} = 15.625$ cubic meters.

Its capacity in liters is $15.625 \times 1,000 = 15,625$ liters.

80% of this is

$15,625 \times 0.8 = 12,500$ liters.

Report an Error

Example Question #834 : Gmat Quantitative Reasoning

Which choice comes closest to the volume of a cube with surface area 135,000 square centimeters?

Possible Answers:

$3 \textup{ m}^{3}$

$3.5 \textup{ m}^{3}$

$4.5 \textup{ m}^{3}$

$4 \textup{ m}^{3}$

$5 \textup{ m}^{3}$

Correct answer:

$3.5 \textup{ m}^{3}$

Explanation:

The suface area of a cube is six times the square of the length of one side, so solve for in the following:

$6s^{2} =135,000$

$s^{2} = 22,500$

s = 150

This is the sidelength in centimeters; since we are looking at meters, divide this by 100 to convert to $150 \div 100 = 1.5$ meters.

Cube this to get volume

$V =1.5^{3}= 3.375$ cubic meters.

Of the given choices, 3.5 cubic meters comes closest.

Report an Error

Example Question #835 : Gmat Quantitative Reasoning

The distance from one vertex of a cube to its opposite vertex is one foot. Give the volume of the cube.

Possible Answers:

$288 \textup{ in}^{3}$

$64 \sqrt{3} \textup{ in}^{3}$

$266 \sqrt{2} \textup{ in}^{3}$

$192 \sqrt{3} \textup{ in}^{3}$

$216 \textup{ in}^{3}$

Correct answer:

$192 \sqrt{3} \textup{ in}^{3}$

Explanation:

Since we are looking at inches, we will look at one foot as twelve inches.

Let be the length of one edge of the cube. By the three-dimensional extension of the Pythagorean Theorem,

$s^{2}+s^{2}+s^{2}=12^{2}$

$3s^{2}=144$

$s^{2}=48$

$s= \sqrt{48} = 4\sqrt{3}$ inches.

Cube this sidelength to get the volume:

$s^{3}= \left ( 4\sqrt{3} \right )^{3} = 4^{3} \cdot \left ( \sqrt{3} \right ) ^{3} = 64 \cdot 3 \sqrt{3}= 192 \sqrt{3}$ cubic inches.

Report an Error

Example Question #831 : Gmat Quantitative Reasoning

A cubic pool is usually filled at about $95\%$ of its total volume. If one side of the pool is m, how many liters of water will fill the pool to the desired capacity?

Possible Answers:

9,500

9,500,000

950,000

950

95,000

Correct answer:

950,000

Explanation:

To find the volume of a cube we use the formula:

V=s^3

In our case the total volume of the pool is 10³cubic meters.

Filling the pool to 95% of its total volume will require: $0.95\times1000 = 950$ cubic meters.

Now we need to convert from cubic meters to liters in order to answer the question.

Remember cubic meter = 1000 liters.

Thus,

$950 \times 1000=950,000$ .

Therefore, the number of liters of water needed is 950000 liters.

Report an Error

Example Question #837 : Gmat Quantitative Reasoning

A sphere of surface area $324 \pi$ is inscribed inside a cube. Give the volume of the cube.

Possible Answers:

5,832

The correct answer is not given among the other responses.

792

648

Correct answer:

5,832

Explanation:

The diameter of a sphere is equal to the length of an edge of the cube in which it is inscribed. We can derive the radius using the formula for the surface area of a sphere:

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

Substituting in the given value:

$4 \pi r^{2} = 324 \pi$

Dividing each side by $4\pi$ :

$r^{2} = \frac{324 \pi}{4 \pi }= 81$

Taking the square root of each side:

r = 9

The diameter is twice this, or . This is the length of the edge of the cube, so we can cube it to get the volume:

$V =18 ^{3}= 5,832$

Report an Error

Example Question #838 : Gmat Quantitative Reasoning

A sphere with surface area $324 \pi$ circumscribes a cube. Give the volume of the cube.

Possible Answers:

5,832

648

The correct answer is not given among the other responses.

792

Correct answer:

The correct answer is not given among the other responses.

Explanation:

The diameter of a sphere is equal to the length of a diagonal of the cube it circumscribes. We can derive the radius using the formula for the volume of a sphere, but first, we have to solve for the radius using the formula for the surface area of a sphere:

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

$4 \pi r^{2} = 324 \pi$

$r^{2} = \frac{324 \pi}{4 \pi }= 81$

r = 9

The diameter is twice this, or . This is the length of the diagonal of the cube. By the three-dimensional extension of the Pythagorean Theorem,

$s^{2}+ s^{2}+ s^{2} = 18^{2}$

$3s^{2} = 324$

$s^{2} =108$

$s = \sqrt{108} = \sqrt{36} \cdot \sqrt{3} = 6 \sqrt{3}$

The volume is the cube of this:

$V =(6 \sqrt{3}) ^{3}= 6^{3} \cdot \left (\sqrt{3} \right )^{3} = 216 \cdot 3 \cdot \sqrt{3} = 648 \sqrt{3}$ , which is not given as one of the choices.

Report an Error

Example Question #839 : Gmat Quantitative Reasoning

A cube has a volume of cubic feet. If the length of each side of the cube is doubled, what is its new volume, in cubic feet?

Possible Answers:

Correct answer:

Explanation:

One way we can solve this problem is by first determining the dimensions of the original cube. By definition, the length, width, and depth of a cube are equal, so if the original volume is 8 cubic feet, then:

$V_o=L_o^3=8\rightarrow L_o=\sqrt[3]{8}=2$

We then double the length of each side of the original cube, so the length of each side of the new cube is:

L=2L_o=2(2)=4

Now we can use the dimensions of our new cube to find its volume:

V=L^3=(4)^3=64

So if we double the dimensions of the original cube, the resulting cube has a volume that is eight times greater, 64 cubic feet.

Report an Error

← Previous 1 2 3 4 Next →

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in Atlanta, SAT Tutors in Chicago, GRE Tutors in Los Angeles, ACT Tutors in New York City, ACT Tutors in Seattle, Computer Science Tutors in Atlanta, Statistics Tutors in Atlanta, Reading Tutors in San Francisco-Bay Area, Physics Tutors in Miami, ACT Tutors in Phoenix

Popular Courses & Classes

Spanish Courses & Classes in New York City, ISEE Courses & Classes in Chicago, SAT Courses & Classes in Seattle, GRE Courses & Classes in Miami, GMAT Courses & Classes in Seattle, Spanish Courses & Classes in Seattle, GRE Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Phoenix, ISEE Courses & Classes in Miami, Spanish Courses & Classes in San Diego

Popular Test Prep

SSAT Test Prep in Philadelphia, LSAT Test Prep in Washington DC, ISEE Test Prep in Chicago, LSAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Philadelphia, MCAT Test Prep in Houston, ACT Test Prep in San Diego, SSAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Phoenix

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)

Email address:
Your name:
Feedback:

GMAT Math : Cubes

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #831 : Gmat Quantitative Reasoning

Example Question #832 : Gmat Quantitative Reasoning

Example Question #833 : Gmat Quantitative Reasoning

Example Question #834 : Gmat Quantitative Reasoning

Example Question #835 : Gmat Quantitative Reasoning

Example Question #831 : Gmat Quantitative Reasoning

Example Question #837 : Gmat Quantitative Reasoning

Example Question #838 : Gmat Quantitative Reasoning

Example Question #839 : Gmat Quantitative Reasoning

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details