GMAT Math : Rectangular Solids & Cylinders

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 #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

Example Question #5 : Calculating The Surface Area Of A Cube

Cube A is inscribed inside a sphere, which is inscribed inside Cube B. Give the ratio of the surface area of Cube B to that of Cube A.

Possible Answers:

4:1

3:1

3:2

2:1

9:4

Correct answer:

3:1

Explanation:

Suppose the sphere has diameter .

Then Cube B, the circumscribing cube, has as its edge length the diameter , and its surface area is $6d^{2}$ .

Also, Cube A, the inscribed cube, has this diameter as the length of its diagonal. If is the length of an edge, then from the three-dimensional extension of the Pythagorean Theorem,

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

$3s^{2} = d^{2}$

The surface area is $SA = 6s^{2}$ , so

$SA = 6s ^{2 } = 2 \cdot 3s^{2} = 2 d^{2}$ .

The ratio of the surface areas is

$\frac{6d^{2}}{ 2 d^{2}} = \frac{3}{1}$

The correct choice is 3:1 .

Report an Error

Example Question #101 : Rectangular Solids & Cylinders

The length of one side of a cube is 4 meters. What is the surface area of the cube?

Possible Answers:

m^2

128 m^2

150 m^2

Correct answer:

m^2

Explanation:

By definition, all sides of a cube are equal in length, so each face is a square, There are six faces on a cube, so its total surface area is six times the area of one of its square faces. If one of its sides is 4 meters, then this will also be the other dimension of one of its square faces, so the total surface area is:

SA=6L^2=6(4)^2=96 m^2

Report an Error

Example Question #101 : Rectangular Solids & Cylinders

Find the surface area of a cube whose side length is .

Possible Answers:

Correct answer:

Explanation:

To solve, remember that the equation for surface area of a cube is:

SA=6s^2=6(4^2)=6*16=96

Report an Error

Example Question #101 : Rectangular Solids & Cylinders

Aperture labs makes a variety of cubes. If each cube has a volume of , what is the surface area of the cube?

Possible Answers:

45.67ft^2

3.30ft^2

19.81ft^2

1.82ft^2

Correct answer:

19.81ft^2

Explanation:

Aperture labs makes a variety of cubes. If each cube has a volume of , what is the surface area of the cube?

Let's work backwards from our goal in this question.

We know that we need to find surface area. To find surface area of a cube, we can use the following equation:

SA=6l^2

Where l is the length of one side.

Next, let's look at the volume formula:

$V_{cube}=l^3$

So, we can find our length

6ft^3=l^3

$l=(6)^{\frac{1}{3}}$

Let's leave l like that for the moment, and use it to find our surface area.

$SA=6((6)^{\frac{1}{3}})^2\approx19.81ft^2$

Report an Error

Example Question #1 : Calculating The Volume Of A Cube

What is the volume of a cube with a side length of ?

Possible Answers:

Correct answer:

Explanation:

V=s^3

V=2^3

V=8

Report an Error

Example Question #102 : Rectangular Solids & Cylinders

The length, width, and height of a rectangular prism, in inches, are three different prime numbers. All three dimensions are between six feet and seven feet. What is the volume of the prism?

Possible Answers:

$504,889\textrm{ in}^{3}$

$444,059\textrm{ in}^{3}$

$478,661 \textrm{ in}^{3}$

$490,779\textrm{ in}^{3}$

It is impossible to tell from the information given.

Correct answer:

$478,661 \textrm{ in}^{3}$

Explanation:

Six feet and seven feet are equal to, respectively, 72 inches and 84 inches. There are three different prime numbers between 72 and 84 - 73, 79, and 83 - so these are the three dimensions of the prism in inches. The volume of the prism is

$73 \times 79 \times 83 = 478,661$ cubic inches.

Report an Error

Example Question #3 : Calculating The Volume Of A Cube

The length of a diagonal of one face of a cube is $5\sqrt{2}$ . Give the volume of the cube.

Possible Answers:

250

$125 \sqrt{2}$

125

$\frac{125 \sqrt{2}}{2}$

The correct answer is not among the other responses.

Correct answer:

125

Explanation:

A diagonal of a square has length $\sqrt{2}$ times that of a side, so each side of each square face of the cube has length $5 \sqrt{2} \div \sqrt{2}= 5$ . Cube this to get the volume:

$V= 5^{3} = 125$

Report an Error

Example Question #4 : Calculating The Volume Of A Cube

The length of a diagonal of a cube is $\sqrt{17}$ . Give the volume of the cube.

Possible Answers:

$\frac{ 17 \sqrt{ 51} }{ 9} \right )$

$\frac{ 17 \sqrt{ 51} }{ 3} \right )$

289

$\frac{ 17 \sqrt{ 34} }{ 2} \right )$

$\frac{ 17 \sqrt{ 34} }{ 6} \right )$

Correct answer:

$\frac{ 17 \sqrt{ 51} }{ 9} \right )$

Explanation:

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

$s^{2}+s^{2}+s^{2}= ( \sqrt{17})^{2}$

$3s^{2}= 17$

$s^{2}= \frac{17}{3}$

$s =\sqrt{ \frac{17}{3}}$

Cube the sidelength to get the volume:

$s^{3} =\left (\sqrt{ \frac{17}{3}} \right )^{3}$

$=\frac{ \left (\sqrt{ 17} \right )^{3}}{\left (\sqrt{3} \right )^{3}} \right )$

$=\frac{ 17 \sqrt{ 17} }{ 3 \sqrt{3} } \right )$

$=\frac{ 17 \sqrt{ 17} \cdot \sqrt{3}}{ 3 \sqrt{3} \cdot \sqrt{3}} \right )$

$=\frac{ 17 \sqrt{ 51} }{ 9} \right )$

Report an Error

Example Question #5 : Calculating The Volume Of A Cube

A sphere with surface area $40 \pi$ is inscribed inside a cube. Give the volume of the cube.

Possible Answers:

8 0

$10 \sqrt{10}$

$40 \sqrt{10}$

$80 \sqrt{10}$

Correct answer:

$80 \sqrt{10}$

Explanation:

The sidelength of the cube is the diameter of the inscribed sphere, which is twice that sphere's radius. The sphere has surface area $40 \pi$ , so the radius is calculated as follows:

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

$4 \pi r^{2} = 40 \pi$

$r^{2} = 40 \pi \div 4 \pi = 10$

$r = \sqrt{10}$

The diameter of the sphere - and the sidelength of the cube - is twice this, or $2 \sqrt{10}$ .

Cube this sidelength to get the volume of the cube:

$V= \left ( 2 \sqrt{10} \right )^{3} = 2^{3} \cdot\left ( \sqrt{10 } \right )^{3} = 8 \cdot 10 \sqrt{10} = 80 \sqrt{10}$

Report an Error

All GMAT Math Resources

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

Popular Subjects

LSAT Tutors in Houston, French Tutors in Seattle, Chemistry Tutors in Denver, SSAT Tutors in Boston, Calculus Tutors in New York City, Reading Tutors in Philadelphia, SAT Tutors in Atlanta, ISEE Tutors in Boston, ISEE Tutors in Phoenix, Biology Tutors in Chicago

Popular Courses & Classes

ACT Courses & Classes in Houston, LSAT Courses & Classes in Boston, GRE Courses & Classes in Miami, ISEE Courses & Classes in Washington DC, GRE Courses & Classes in Philadelphia, GRE Courses & Classes in Washington DC, ISEE Courses & Classes in Boston, SSAT Courses & Classes in New York City, LSAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

ACT Test Prep in Houston, GRE Test Prep in Denver, SAT Test Prep in Washington DC, ISEE Test Prep in New York City, ISEE Test Prep in Phoenix, GMAT Test Prep in Boston, GMAT Test Prep in New York City, ISEE Test Prep in Boston, ACT Test Prep in Los Angeles, ACT 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)

Email address:
Your name:
Feedback:

GMAT Math : Rectangular Solids & Cylinders

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #816 : Gmat Quantitative Reasoning

Example Question #5 : Calculating The Surface Area Of A Cube

Example Question #101 : Rectangular Solids & Cylinders

Example Question #101 : Rectangular Solids & Cylinders

Example Question #101 : Rectangular Solids & Cylinders

Example Question #1 : Calculating The Volume Of A Cube

Example Question #102 : Rectangular Solids & Cylinders

Example Question #3 : Calculating The Volume Of A Cube

Example Question #4 : Calculating The Volume Of A Cube

Example Question #5 : Calculating The Volume Of A Cube

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details