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

Example Question #571 : Geometry

A given cube has an edge length of . What is the length of the diagonal of the cube?

Possible Answers:

$18\sqrt{2}$

$9\sqrt{3}$

$9\sqrt{2}$

Not enough information provided

$18\sqrt{3}$

Correct answer:

$9\sqrt{3}$

Explanation:

The diagonal of a cube with an edge length can be defined by the equation $d=s\sqrt{3}$ . Given s=9 in this instance, $d=9\sqrt{3}$ .

Report an Error

Example Question #571 : Geometry

A given cube has an edge length of $\sqrt{3}$ . What is the length of the diagonal of the cube?

Possible Answers:

$3\sqrt{3}$

None of the above

$2\sqrt{3}$

Correct answer:

Explanation:

The diagonal of a cube with an edge length can be defined by the equation $d=s\sqrt{3}$ . Given $s=\sqrt{3}$ in this instance, $d=\sqrt{3}\left ( \sqrt{3} \right )=3$ .

Report an Error

Example Question #1 : Calculating The Diagonal Of A Cube

If a cube has a side length of , what is the length of its diagonal?

Possible Answers:

$4\sqrt{3}$

$3\sqrt{2}$

$3\sqrt{4}$

$2\sqrt{3}$

$4\sqrt{2}$

Correct answer:

$4\sqrt{3}$

Explanation:

The diagonal of a cube is the hypotenuse of a right triangle whose height is one side and whose base is the diagonal of one of the faces. First we must use the Pythagorean theorem to find the length of the diagonal of one of the faces, and then we use the theorem again with this value and length of one side of the cube to find the length of its diagonal:

a^2+b^2=c^2

4^2+4^2=c^2

$c^2=32\rightarrow c=\sqrt{32}$

So this is the length of the diagonal of one of the faces, which we plug into the Pythagorean theorem with the length of one side to find the length of the diagonal for the cube:

h^2+c^2=d^2

$4^2+(\sqrt{32})^2=d^2$

$d^2=48\rightarrow d=\sqrt{48}=\sqrt{3*16}=4\sqrt{3}$

Report an Error

Example Question #11 : Cubes

What is the surface area of a box that is 3 feet long, 2 feet wide, and 4 feet high?

Possible Answers:

$\dpi{100} \small 40$

$\dpi{100} \small 43$

$\dpi{100} \small 60$

$\dpi{100} \small 52$

$\dpi{100} \small 24$

Correct answer:

$\dpi{100} \small 52$

Explanation:

$\dpi{100} \small SA = 2lw + 2lh + 2wh = 2\times 3\times 2 + 2 \times 3\times 4 + 2\times 2\times 4 = 52$

Report an Error

Example Question #12 : Cubes

What is the surface area of a cube with side length 4?

Possible Answers:

384

Correct answer:

Explanation:

$SA=6\ast side^{2}=6\ast 4^{2}=6\ast 16=96$

Report an Error

Example Question #2 : Calculating The Surface Area Of A Cube

The surface area of a certain cube is 150 square feet. If the width of the cube is increased by 2 feet, the length decreased by 2 feet and the height increased by 1 foot, what is the new surface area?

Possible Answers:

$192\ ft^{2}$

$252\ ft^{2}$

$162\ ft^{2}$

$243\ ft^{2}$

$151\ ft^{2}$

Correct answer:

$162\ ft^{2}$

Explanation:

The first step to answering this qestion is to determine the original length of the sides of the cube. The surface area of a cube is given by:

$S_{A} = 6x^{2}$

Where is the length of each side. This tells us that for our cube:

$150 = 6x^{2}$ ==> $25 = x^{2}$ ==> x = 5

If the width increases by 2, the length decreases by 2 and the height increases by 1:

w=7 , l=3 , h=6

We now have a rectangular prism. The surface area of a rectangular prism is given by:

$S_{A} = 2(wl + lh + hw)$

For our prism:

$2((7\times 3) + (7 \times 6) + (6 \times 3)) = 2(21 + 42 + 18) = 162$

Report an Error

Example Question #13 : Cubes

What is the surface area of a cube with a side length of ?

Possible Answers:

Correct answer:

Explanation:

SA=6s^2

SA=6(2)^2

SA=6*4

SA=24

Report an Error

Example Question #3 : Calculating The Surface Area Of A Cube

A cube is inscribed inside a sphere with surface area $100 \pi$ . Give the volume of the cube.

Possible Answers:

500

$250 \sqrt{2}$

$\frac{1,000 \sqrt{2} } {6 }$

$250 \sqrt{2}$

$\frac{1,000 \sqrt{3} } {9 }$

Correct answer:

$\frac{1,000 \sqrt{3} } {9 }$

Explanation:

Each diagonal of the inscribed cube is a diameter of the sphere, so its length is the sphere's diameter, or twice its radius.

The sphere has surface area $80 \pi$ , so the radius is calculated as follows:

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

$4 \pi r^{2} = 100 \pi$

$r^{2} =100 \pi \div 4 \pi = 25$

r = 5

The diameter of the circle - and the length of a diagonal of the cube - is twice this, or 10.

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

$s^{2}+s^{2}+s^{2}=10^{2}$

$3s^{2}=100$

$s^{2}=\frac{100}{3}$

$s = \sqrt{\frac{100}{3}} = \frac{\sqrt{100}}{\sqrt{3}} = \frac{10}{\sqrt{3}}$

The volume of the cube is the cube of this, or

$V=\left ( \frac{10}{\sqrt{3}} \right )^{3} = \frac{10^{3} } {\left (\sqrt{3} \right )^{3} } =\frac{1,000 } {3 \sqrt{3} } =\frac{1,000 \cdot \sqrt{3} } {3 \sqrt{3} \cdot \sqrt{3} } =\frac{1,000 \sqrt{3} } {9 }$

Report an Error

Example Question #6 : Calculating The Surface Area Of A Cube

A sphere of volume $28 8 \pi$ is inscribed inside a cube. Give the surface area of the cube.

Possible Answers:

216

144

288

864

Correct answer:

864

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 volume formula:

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

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

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

$\frac{3}{4} \cdot \frac{4}{3} r^{3} = \frac{3}{4} \cdot 288$

$r^{3} = 216$

r = 6

Twice this, or 12, is the diameter, and, subsequently, the length of an edge of the cube. If s = 12 , the surface area is

$A = 6s^{2} = 6 \cdot 12^{2}= 6 \cdot 144 = 864$

Report an Error

Example Question #816 : Gmat Quantitative Reasoning

A cube is inscribed inside a sphere of volume $2 88 \pi$ . Give the surface area of the cube.

Possible Answers:

864

288

144

216

Correct answer:

288

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 volume formula:

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

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

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

$\frac{3}{4} \cdot \frac{4}{3} r^{3} = \frac{3}{4} \cdot 288$

$r^{3} = 216$

r = 6

Twice this, or 12, is the diameter, and, subsequently, the length of a diagonal of the cube. By an extension of the Pythagorean Theorem, if is the length of an edge of the cube,

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

$3s^{2} = 144$

$s^{2} = 48$

The surface area is six times this:

$SA = 6s^{2} = 6 \cdot 48 = 288$

Report an Error

All GMAT Math Resources

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

Popular Subjects

SSAT Tutors in San Diego, Reading Tutors in Miami, Biology Tutors in Philadelphia, English Tutors in Miami, LSAT Tutors in Washington DC, ISEE Tutors in Philadelphia, Statistics Tutors in Los Angeles, SSAT Tutors in Philadelphia, Algebra Tutors in Miami, ISEE Tutors in Boston

Popular Courses & Classes

LSAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Denver, ACT Courses & Classes in Chicago, LSAT Courses & Classes in Atlanta, MCAT Courses & Classes in San Diego, SSAT Courses & Classes in Philadelphia, GRE Courses & Classes in Atlanta, ISEE Courses & Classes in Los Angeles, GMAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in New York City

Popular Test Prep

GMAT Test Prep in Denver, SAT Test Prep in Denver, MCAT Test Prep in San Diego, ACT Test Prep in Chicago, SAT Test Prep in Boston, LSAT Test Prep in New York City, LSAT Test Prep in Phoenix, LSAT Test Prep in Houston, MCAT Test Prep in Atlanta, ISEE 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)

Email address:
Your name:
Feedback:

GMAT Math : Cubes

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #571 : Geometry

Example Question #571 : Geometry

Example Question #1 : Calculating The Diagonal Of A Cube

Example Question #11 : Cubes

Example Question #12 : Cubes

Example Question #2 : Calculating The Surface Area Of A Cube

Example Question #13 : Cubes

Example Question #3 : Calculating The Surface Area Of A Cube

Example Question #6 : Calculating The Surface Area Of A Cube

Example Question #816 : Gmat Quantitative Reasoning

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details