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

← Previous 1 2 3 4 5 6 7 8 Next →

Example Question #1 : Dsq: Calculating The Volume Of A Cylinder

How much water, in cubic feet, can a cylindrical water tank whose bases have radius 6 feet hold?

Statement 1: The lateral area of the tank is 125.66 square yards.

Statement 2: The tank is 30 feet high.

Possible Answers:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is not sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is not sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

We are given the radius; if we know the height, we can use the formula

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

to calculate the volume of the tank.

The second statement gives us that the tank is 30 feet high. But the first statement gives us the way to find the height by using the lateral area formula.

First we have to convert square yards to square feet by multiplying by 9.

$125.66 \cdot 9 = 1,130.94$

$L.A.= 2\pi rh$

$1,130.94= 2\pi \cdot 6\cdot h= 12\pi h$

$h=\frac{ 1,130.94}{12\pi }=30$

Either way, we now have both radius and height, and we can find the volume:

$V=\pi \cdot 6^{2} \cdot 30 \approx 3392.9$

The answer is that either statement alone is sufficient to answer the question.

Report an Error

Example Question #1 : Dsq: Calculating The Length Of An Edge Of A Cube

What is the length of the edge of a cube?

1) Its volume is 1,728 cubic meters.

2) Its surface area is 864 square meters

Possible Answers:

Statement 1 ALONE is sufficient, but Statement 2 alone is not sufficient.

Statements 1 and 2 TOGETHER are not sufficient.

BOTH statements TOGETHER are sufficient, but neither statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statement 2 ALONE is sufficient, but Statement 1 alone is not sufficient.

Correct answer:

EACH statement ALONE is sufficient.

Explanation:

Call the sidelength, surface area, and volume of the cube , , and , respectively.

Then

$V = s^{3}$

or, equivalently,

$s = \sqrt[3]{V}$

So, given statement 1 alone - that is, given only the volume, you can demonstrate the sidelength to be

$s = \sqrt[3]{1,728} = 12$

Also,

$A = 6s^{2}$

or, equivalently,

$s = \sqrt{\frac{A}{6}}$

Given statement 2 alone - that is, given only the surface area, you can demonstrate the sidelength to be

$s = \sqrt{\frac{864}{6}} = \sqrt{144} = 12$

Therefore, the answer is that either statement alone is sufficient.

Report an Error

Example Question #51 : Rectangular Solids & Cylinders

A sphere is inscribed inside a cube. What is the volume of the sphere?

Statement 1: The surface area of the cube is 216.

Statement 2: The volume of the cube is 216.

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

The diameter of a sphere inscribed inside a cube is equal to the length of one of the edges of a cube. From either the surface area or the volume of a cube, the appropriate formula can be used to calculate this length. Half this is the radius, from which the formula $V = \frac{4}{3} \pi r^{3}$ can be used to find the volume of the sphere.

Report an Error

Example Question #3 : Dsq: Calculating The Length Of An Edge Of A Cube

What is the length of edge of cube ABCDEFGH ?

(1) $HB=6\sqrt{3}$ .

(2) $\measuredangle {EHB}=45^{\circ}$ .

Possible Answers:

Statement 2 alone is sufficient.

Statements 1 and 2 together are not sufficient.

Statement 1 alone is sufficient.

Each statement alone is sufficient.

Both statements together are sufficient.

Correct answer:

Statement 1 alone is sufficient.

Explanation:

In order to find the length of an edge, we would need any information about one of the faces of the cube or about the diagonal of the cube.

Statement 1 gives us the length of the diagonal of the cube, since the formula for the diagonal is $d=s\sqrt{3}$ where is the length of an edge of the cube and is the length of the diagonal we are able to find the length of the edge. Therefore statement 1 alone is sufficient.

Statement 2 alones is insufficient, it gives us something we can already tell knowing that ABCDEFGH is a cube.

Statement 1 alone is sufficient.

Report an Error

Example Question #4 : Dsq: Calculating The Length Of An Edge Of A Cube

ABCDEFGH is a cube. What is the length of edge ?

(1) The volume of the cube is .

(2) The area of face ABCD is .

Possible Answers:

Both statements together are sufficient.

Statement 1 alone is sufficient.

Statement 2 alone is sufficient.

Statements 1 and 2 together are not sufficient.

Each statement alone is sufficient.

Correct answer:

Each statement alone is sufficient.

Explanation:

Like we have previously seen, to find the length of an edge, we need to have information about the other faces or anything else within the cube.

Statement 1 tells us that the volume of the cube is , from this we can find the length of the side of the cube. Statement 1 alone is sufficient.

Statement 2, tells us that the area of ABCD is , similarily, by taking the square root of this number, we can find the length of the edge of the cube.

Therefore each statement alone is sufficient.

Report an Error

Example Question #5 : Dsq: Calculating The Length Of An Edge Of A Cube

Find the length of an edge of the cube.

The volume of the cube is .
The surface area of the cube is .

Possible Answers:

Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

Each statement alone is sufficient to answer the question.

Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.

Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.

Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.

Correct answer:

Each statement alone is sufficient to answer the question.

Explanation:

Statement 1: Use the volume formula for a cube to solve for the side length.

V=a^3=125 where represents the length of the edge

$a=\sqrt[3]{125}=5cm$

Statement 2: Use the surface area formula for a cube to solve for the side length.

SA=6a^2=150

a^2=25

a=5cm

Each statement alone is sufficient to answer the question.

Report an Error

Example Question #1 : Dsq: Calculating The Diagonal Of A Cube

ABCDEFGH is a cube. What is the length of diagonal ?

(1) The area of a face of the cube is .

(2) The length of is $3\sqrt{2}$ .

Possible Answers:

Both statements taken together are sufficient.

Statement 1 alone is sufficient.

Statement 2 alone is sufficient.

Statements 1 and 2 taken together are not sufficient.

Each statement alone is sufficient.

Correct answer:

Each statement alone is sufficient.

Explanation:

To know the diagonal HB of the cube, we need to have information about the length of the edges of the cube. Knowing the area of a face would allow us to find the length of an edge; therefore statement 1 alone is sufficient.

Statment 2 alone is sufficient as well since the length of a diagonal of a square is given by $s\sqrt{2}$ , where is the length of a side of the square and ultimately we can find the length of an edge of the square.

Therefore each statement alone is sufficient.

Report an Error

Example Question #2 : Dsq: Calculating The Diagonal Of A Cube

Calculate the diagonal of a cube.

The surface area of the cube is .
The volume of the cube is .

Possible Answers:

Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.

Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.

Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.

Each statement alone is sufficient to answer the question.

Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

Correct answer:

Each statement alone is sufficient to answer the question.

Explanation:

Statement 1: We can use the surface area to find the length of the cube's edge and then determine the length of the diagonal.

SA=6a^2=96

where represents the length of the cube's edge

a^2=16

a=4

Now that we know the length of the edge, we can find the length of the diagonal: $d=a\sqrt{3}=4\sqrt{3}cm$ .

Statement 2: Once again, we can use the provided information to find the length of the cube's edge.

V=a^3=64

$a=\sqrt[3]{64}=4$

Which means the length of the diagonal is $d=a\sqrt{3}=4\sqrt{3} cm$ .

Thus, each statement alone is sufficient to answer the question.

Report an Error

Example Question #3 : Dsq: Calculating The Diagonal Of A Cube

Give the length of the diagonal of the cube.

The surface area of the cube is .
The volume of the cube is .

Possible Answers:

Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.

Each statement alone is sufficient to answer the question.

Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.

Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.

Correct answer:

Each statement alone is sufficient to answer the question.

Explanation:

Statement 1: To find the length of the diagonal of the cube we need to find the length of the cube's edge. We can use the given surface area value to do so:

SA=6a^2=294

a^2=49

a=7

Now that we know the length of the cube's edge, we can calculate the diagonal:

$d=a\sqrt{3}=7\sqrt{3}\approx 12.12cm$

Statement 2: We're given the volume of the cube which we can also use to solve for the length of the cube's edge.

a^3=343

$a=\sqrt[3]{343}=7$

Knowing the length of the cube's edge allows us to calculate the diagonal:

$d=a\sqrt{3}=7\sqrt{3}\approx 12.12cm$

Each statement alone is sufficient to answer the question.

Report an Error

Example Question #4 : Dsq: Calculating The Diagonal Of A Cube

Find the diagonal of the cube.

The surface area of the cube is .
The length of an edge of the cube measures .

Possible Answers:

Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.

Each statement alone is sufficient to answer the question.

Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.

Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.

Correct answer:

Each statement alone is sufficient to answer the question.

Explanation:

Statement 1: We need the length of an edge in order to find the diagonal of the cube. Luckily, we can find the length using the information provided:

SA=6a^2=726

a^2=121

a=11

Now that we know the length of an edge is 11 cm we can find the length of the diagonal.

$d=a\sqrt{3}=11\sqrt{3}cm$

Statement 2: We're given the information we need to find the diagonal, all we need to do is plug it into the equation

$d=a\sqrt{3}=11\sqrt{3}cm$

Report an Error

← Previous 1 2 3 4 5 6 7 8 Next →

All GMAT Math Resources

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

Popular Subjects

Physics Tutors in Phoenix, ACT Tutors in San Francisco-Bay Area, Statistics Tutors in San Francisco-Bay Area, Algebra Tutors in Phoenix, MCAT Tutors in Atlanta, Math Tutors in Atlanta, Biology Tutors in Miami, MCAT Tutors in San Diego, French Tutors in Chicago, Biology Tutors in Houston

Popular Courses & Classes

LSAT Courses & Classes in Seattle, Spanish Courses & Classes in Miami, ACT Courses & Classes in Denver, LSAT Courses & Classes in Philadelphia, SAT Courses & Classes in Los Angeles, ACT Courses & Classes in Phoenix, Spanish Courses & Classes in Washington DC, Spanish Courses & Classes in Philadelphia, ACT Courses & Classes in Boston, ISEE Courses & Classes in Dallas Fort Worth

Popular Test Prep

ACT Test Prep in Denver, SSAT Test Prep in Dallas Fort Worth, ACT Test Prep in New York City, ACT Test Prep in Boston, GMAT Test Prep in Seattle, MCAT Test Prep in Miami, SAT Test Prep in New York City, SAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Phoenix, GRE Test Prep in Denver

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 #1 : Dsq: Calculating The Volume Of A Cylinder

Example Question #1 : Dsq: Calculating The Length Of An Edge Of A Cube

Example Question #51 : Rectangular Solids & Cylinders

Example Question #3 : Dsq: Calculating The Length Of An Edge Of A Cube

Example Question #4 : Dsq: Calculating The Length Of An Edge Of A Cube

Example Question #5 : Dsq: Calculating The Length Of An Edge Of A Cube

Example Question #1 : Dsq: Calculating The Diagonal Of A Cube

Example Question #2 : Dsq: Calculating The Diagonal Of A Cube

Example Question #3 : Dsq: Calculating The Diagonal Of A Cube

Example Question #4 : Dsq: Calculating The Diagonal Of A Cube

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details