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 #14 : Dsq: Calculating The Surface Area Of A Cylinder

Of a given cylinder and a given cube, which, if either, has the greater surface area?

Statement 1: Both the height of the cylinder and the diameter of its bases are equal to the length of one edge of the cube.

Statement 2: Each face of the cube has as its area four times the square of the radius of the bases of the cylinder.

Possible Answers:

EITHER 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.

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

BOTH statements TOGETHER are insufficient 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:

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

Explanation:

The surface area of a cylinder, given height and radius of the bases , is given by the formula

$A =2 \pi r (r+h)$

The surface area of a cube, given the length of each edge, is given by the formula

$A ' = 6s^{2}$ .

Assume Statement 1 alone. Then h = s and, since the diameter of a base is , the radius is half this, or $r = \frac{1}{2}s$ . The surface area of the cylinder is, in terms of , equal to

$A =2 \pi s \left ( s+ \frac{1}{2}s \right )= 2 \pi s \cdot \frac{3}{2}s = 3 \pi s^{2}$ .

Since $3 \pi > 6$ , the cylinder has the greater area regardless of the actual measurements.

Assume Statement 2 alone. The cube has six faces with area $4r^{2}$ , so its surface area is six times this, or $6 \cdot 4r^{2} = 24 r^{2}$ . The surface area of the cylinder is $A =2 \pi r (r+h) = 2 \pi r^{2}+ 2 \pi rh$ ; however, without knowing anything aobout the height of the cylinder, we cannot compare the two surface areas.

Report an Error

Example Question #15 : Dsq: Calculating The Surface Area Of A Cylinder

Of Cylinder 1 and Cylinder 2, which, if either, has the greater surface area?

Statement 1: The radius of the bases of Cylinder 1 is equal to the height of Cylinder 2.

Statement 2: The radius of the bases of Cylinder 2 is equal to the height of Cylinder 1.

Possible Answers:

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

BOTH statements TOGETHER are insufficient to answer the question.

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.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

The surface area of the cylinder can be calculated from radius and height using the formula:

$A = 2 \pi rh + 2 \pi r^{2}$ .

We show that both statements together provide insufficient information by first noting that if the two cylinders have the same height, and their bases have the same radius, their surface areas will be the same.

Now we explore the case in which Cylinder 1 has height 6 and bases with radius 8, and Cylinder 2 has height 8 and bases of radius 6.

The surface area of Cylinder 1 is

$A = 2 \pi \cdot 8 \cdot 6 + 2 \pi \cdot 8^{2}$

$= 2 \pi \cdot 8 \cdot 6 + 2 \pi \cdot 8 \cdot 8$

$=96 \pi + 128 \pi$

$=224 \pi$

The surface area of Cylinder 2 is

$A = 2 \pi \cdot 6 \cdot 8 + 2 \pi \cdot 6^{2}$

$= 2 \pi \cdot 6 \cdot 8 + 2 \pi \cdot 6 \cdot 6$

$=96 \pi + 72\pi$

$=168\pi$

In this scenario, Cylinder 1 has the greater surface area.

Report an Error

Example Question #16 : Dsq: Calculating The Surface Area Of A Cylinder

Inscribed_cylinder

In the above figure, a cylinder is inscribed inside a cube. What is the surface area of the cylinder?

Statement 1: The volume of the cube is 729.

Statement 2: The surface area of the cube is 486.

Possible Answers:

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

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient 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.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

The surface area of the cylinder can be calculated from radius and height using the formula:

$A = 2 \pi rh + 2 \pi r^{2}$ .

It can be seen from the diagram that if we let be the length of one edge of the cube, then h = s and $r = \frac{1}{2}s$ . The surface area formula can be rewritten as

$A = 2 \pi \cdot \frac{1}{2}s \cdot s + 2 \pi \left ( \frac{1}{2}s \right ) ^{2}$

$A = \pi s ^{2}+ 2 \pi \cdot \frac{1}{4}s ^{2}$

$A = \pi s ^{2}+ \frac{1}{2} \pi s ^{2}$

$A = \frac{3}{2} \pi s ^{2}$

Subsequently, the length of one edge of the cube is sufficient to calculate the surface area of the cylinder.

From Statement 1 alone, the length of an edge of the cube can be calculated using the volume formula:

$s^{3} = V = 729$

$s = \sqrt[3]{729}= 9$

From Statement 2 alone, the length of an edge of the cube can be calculated using the surface area formula:

$6s^{2} = A = 486$

$s^{2}= 486 \div 6 = 81$

$s = \sqrt{81}= 9$

Since can be calculated from either statement alone, so can the surface area of the cylinder:

$A = \frac{3}{2} \pi s ^{2} = \frac{3}{2} \pi \cdot 9 ^{2} = \frac{243}{2} \pi$

Report an Error

Example Question #211 : Geometry

Of two given solids - a cylinder and a regular triangular prism - which has the greater surface area?

Statement 1: Each side of a triangular base of the prism has length one third the circumference of a base of the cylinder.

Statement 2: The cylinder and the prism have the same height.

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

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

BOTH statements TOGETHER are insufficient to answer the question.

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.

Correct answer:

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

Explanation:

Statement 1 alone provides insufficient information. The surface area of a cylinder with bases of radius and height is

$a = 2 \pi r ^{2}+ 2 \pi r h$ .

The surface area of a regular triangular prism with height and whose (equilateral triangular) bases have common sidelength - and perimeter - is

$A = 2 \cdot \frac{S^{2}\sqrt{3}}{4} + 3S \cdot H$ , or

$A = \frac{S^{2}\sqrt{3}}{2} + 3S H$ .

Statement 1 alone tells us that $S = \frac{1}{3} \cdot 2 \pi r$ , or $S = \frac{2 \pi }{3} r$ . However, without any information about the heights, we cannot compare and . Similarly, Statement 2 alone tells us that h = H , but nothing about or .

However, if we combine what we know from Statement 2 with the information from Statement 1, we can answer the question. The surface area of a cylinder or a prism is equal to its lateral area plus the areas of its two congruent bases.

The lateral area of a cylinder or a prism is the height multiplied by the perimeter or circumference of a base. From Statement 1, the circumference of the bases of the cylinder is equal to the perimeter of the bases of the prism, and from Statement 2, the heights are equal. It follows that the lateral areas are equal, and that the figure with the bases that are greater in area has the greater surface area.

For simplicity's sake, we will assume that the circumference of the base of the cylinder is $6 \pi$ , for reasons that will be apparent later; this reasoning works for any circumference. The radius of this base is $6 \pi \div 2 \pi = 3$ , and the area is $\pi \cdot 3^{2} = 9 \pi$ . The perimeter of the triangular base of the prism is also $6 \pi$ , so its sidelength is $2 \pi$ , making its area $\frac{(2 \pi)^{2}\sqrt{3}}{2} = 2 \pi^{2}\sqrt{3}$ , which is greater than $9 \pi$ . This makes the prism the greater in surface area as well.

Report an Error

Example Question #41 : Rectangular Solids & Cylinders

What is the volume of the cylinder?

Statement 1: the cylinder has a radius of 3

Statement 2: the cylinder has a height of 4

Possible Answers:

EACH statement ALONE is sufficient.

Statements 1 and 2 TOGETHER are NOT sufficient.

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

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

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

Correct answer:

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

Explanation:

The formula for the volume of a cylinder is: $volume = \Pi \ast r^{2}\ast h$

Therefore we need both Statement 1 and 2 to find the volume, so both statements together are sufficient, but neither statement alone is sufficient.

Report an Error

Example Question #42 : Rectangular Solids & Cylinders

Give the radius of a cylinder with volume 1,000 cubic inches.

1) Its height is 40 inches.

2) The area of its base is 25 square inches.

Possible Answers:

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

BOTH statements TOGETHER are NOT sufficient to answer the question.

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

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

EITHER Statement 1 or Statement 2 ALONE is sufficient to answer the question.

Correct answer:

EITHER Statement 1 or Statement 2 ALONE is sufficient to answer the question.

Explanation:

The two statements are actually equivalent; if $\small V$ is its volume, $\small B$ is the area of its base, and $\small h$ is its height, then $\small V= B h$ , or $\small B=\frac{V}{h}$ . So if we know the first statement, that is, $\small h=40$ , then $\small B=\frac{1,000}{40} = 25$ , which is the second statement.

To find the radius, use $\small B = \pi r^{2}$ , or, equivalently, $\small r =\sqrt{\frac{B}{\pi }}$

$\small \small \small r =\sqrt{\frac{B}{\pi }}=\sqrt{\frac{25}{\pi }} \approx 2.8$

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

Report an Error

Example Question #43 : Rectangular Solids & Cylinders

A factory makes two sizes of cylindrical barrels. How many small cylindrical barrels full of liquid would it take to fill a large barrel?

Statement 1: A large cylindrical barrel is twice as high as a small cylindrical barrel.

Statement 2: A large cylindrical barrel is three times as wide as a small cylindrical barrel.

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are NOT sufficient to answer the question.

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

Correct answer:

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

Explanation:

The question is essentially this: if $V_{S} , V_{L}$ are the volumes of the barrels, then find such that

$V_{L} = KV_{S}$ ,

$\frac{V_{L}}{V_{S}} = K$

Equivalently,

$\frac{ \pi r_{L}^{2} h_{L} }{ \pi r_{S}^{2} h_{S} } = K$

$K = \left ( \frac{ r_{L} } {r_{S} }\right ) ^{2} \cdot \frac{ h_{L} } {h_{S} }$

This means that knowing both the ratio of the heights and the ratio of the radii (and subsequently, the widths) is necessary and sufficient. Therefore, you need both statements, and both together are sufficient.

Report an Error

Example Question #44 : Rectangular Solids & Cylinders

Which of Cylinder 1 and Cylinder 2, if either, has the greater volume?

Statement 1: The height of Cylinder 1 is equal to the radius of the base of Cylinder 2.

Statement 2: The height of Cylinder 2 is equal to twice the radius of the base of Cylinder 1.

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

EITHER 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 sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

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

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Assume both statements. We show that insufficient information is provided using two cases.

Case 1: Cylinder 1 has height 10 and radius 20. Then Cylinder 2 has height 40 and radius 10.

The volume of Cylinder 1 is $V = \pi r ^{2} h = \pi \cdot 20 ^{2} \cdot 10 = 8,000\pi$

The volume of Cylinder 2 is $V = \pi r ^{2} h = \pi \cdot 10 ^{2} \cdot 40 = 4,000\pi$

Case 2: Cylinder has height 40 and radius 10. Then Cylinder 2 has height 20 and radius 40.

The volume of Cylinder 1 is $V = \pi r ^{2} h = \pi \cdot 10 ^{2} \cdot 40 = 4,000\pi$

The volume of Cylinder 2 is $V = \pi r ^{2} h = \pi \cdot 40 ^{2} \cdot 20 = 32,000\pi$

In one case, Cylinder 1 had greater volume; in the other, Cylinder 2 did. This makes the two statements insufficient.

Report an Error

Example Question #21 : Cylinders

How many identical cans can be packed in a certain box?

(1) The box is centimeters wide and centimeters high.

(2) Each can is centimeters high.

Possible Answers:

C: BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient

B: Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient

E: Statements (1) and (2) TOGETHER are not sufficient

D: EACH statement ALONE is sufficient

A: Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient

Correct answer:

E: Statements (1) and (2) TOGETHER are not sufficient

Explanation:

(1) does not give us any information about the cans' dimension or the length of the box, so it is not sufficient alone.

(2) does not give us box dimensions or any information about the cans' diameter, so it is not sufficient alone.

Both statement taken together give more information but we still dont have complete dimensions for the box or each can.

Therefore the right answer is E.

Report an Error

Example Question #22 : Cylinders

Jenkins has a poster tube which he is using to carry his posters to college.

I) The poster tube has a volume of 46 in^3 .

II) The poster tube is inches long.

What is the radius of the poster tube?

Possible Answers:

Both statements are necessary to answer the question.

Neither I nor II are sufficient to answer the question. More information is needed.

Either statement alone is sufficient to answer the question.

Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.

Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.

Correct answer:

Both statements are necessary to answer the question.

Explanation:

Recall the formula for volume of a cylinder:

$\small V=\pi r^2h$

Statement I gives us V

Statement II gives us h

We can then use both of them to find our "r." We cannot do it without both of them.

Report an Error

All GMAT Math Resources

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

Popular Subjects

MCAT Tutors in San Diego, Statistics Tutors in Los Angeles, Physics Tutors in Atlanta, ACT Tutors in New York City, Spanish Tutors in San Diego, Math Tutors in Phoenix, Biology Tutors in Dallas Fort Worth, SAT Tutors in New York City, Math Tutors in Philadelphia, MCAT Tutors in Houston

Popular Courses & Classes

ACT Courses & Classes in Philadelphia, GRE Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Atlanta, SSAT Courses & Classes in Washington DC, LSAT Courses & Classes in New York City, GRE Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in San Diego, LSAT Courses & Classes in Phoenix, ISEE Courses & Classes in Philadelphia, Spanish Courses & Classes in Denver

Popular Test Prep

LSAT Test Prep in Houston, ACT Test Prep in Dallas Fort Worth, ISEE Test Prep in Miami, SAT Test Prep in Los Angeles, GMAT Test Prep in Dallas Fort Worth, GRE Test Prep in Phoenix, LSAT Test Prep in Philadelphia, GRE Test Prep in San Francisco-Bay Area, MCAT Test Prep in Houston, ACT Test Prep in Atlanta

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 #14 : Dsq: Calculating The Surface Area Of A Cylinder

Example Question #15 : Dsq: Calculating The Surface Area Of A Cylinder

Example Question #16 : Dsq: Calculating The Surface Area Of A Cylinder

Example Question #211 : Geometry

Example Question #41 : Rectangular Solids & Cylinders

Example Question #42 : Rectangular Solids & Cylinders

Example Question #43 : Rectangular Solids & Cylinders

Example Question #44 : Rectangular Solids & Cylinders

Example Question #21 : Cylinders

Example Question #22 : Cylinders

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details