Call Now to Set Up Tutoring:

(888) 888-0446

SSAT Upper Level Math : How to find the volume of a cube

Study concepts, example questions & explanations for SSAT Upper Level Math

Create An Account

All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find The Volume Of A Cube

A cube has six square faces, each with area 64 square inches. Using the conversion factor 1 inch = 2.5 centimeters, give the volume of this cube in cubic centimeters, rounding to the nearest whole number.

Possible Answers:

400 cubic centimeters

2,000 cubic centimeters

4,000 cubic centimeters

8,000 cubic centimeters

800 cubic centimeters

Correct answer:

8,000 cubic centimeters

Explanation:

The volume of a cube is the cube of its sidelength, which is also the sidelength of each square face. This sidelength is the square root of the area 64:

$\sqrt{64}=8$ inches.

Multiply this by 2.5 to get the sidelength in centimeters:

$\times 2.5$ = 20 centimeters.

The cube of this is

$20^{3}$ =8000 cubic centimeters

Report an Error

Example Question #1 : How To Find The Volume Of A Cube

A cube has a side length of 5 inches. Give the volume and surface area of the cube.

Possible Answers:

25 in^3 ,150 in^2

125 in^3 ,150 in^2

125 in^3 ,75 in^2

250in^3, 150 in^2

25 in^3 ,75 in^2

Correct answer:

125 in^3 ,150 in^2

Explanation:

A cube has all edges the same length. The volume of a cube is found by multiplying the length of any edge by itself twice. As a formula:

Volume=s^3 where is the length of any edge of the cube.

The Surface Area of a cube can be calculated as 6s^2 .

So we get:

Volume =s^3=5^3=125 in^3

Surface area $=6s^2=6\times 5^2=6\times 25=150 in^2$

Report an Error

Example Question #2 : How To Find The Volume Of A Figure

A cheese seller has a 2 foot x 2 foot x 2 foot block of gouda and she wants to cut it into smaller gouda cubes that are 1.5 inches on a side. How many cubes can she cut?

Possible Answers:

4096

256

512

2048

1024

Correct answer:

4096

Explanation:

First we need to determine how many of the small cubes of gouda would fit along one dimension of the large cheese block. One edge of the large block is 24 inches, so 16 smaller cubes $(24\div 1.5)$ would fit along the edge. Now we simply cube this one dimension to see how many cubes fit within the whole cube. $16^{3}=4096$ .

Report an Error

Example Question #4 : How To Find The Volume Of A Cube

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

Possible Answers:

$\frac{N^{3} \sqrt{2} }{4}$

$\frac{N^{3} }{3 }$

$\frac{N^{3} }{2 }$

$3N\sqrt{N}$

$\frac{N^{3} \sqrt{3} }{9 }$

Correct answer:

$\frac{N^{3} \sqrt{3} }{9 }$

Explanation:

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

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

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

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

$s =\sqrt{\frac{N^{2}}{3}} = \frac{N}{\sqrt{3}} = \frac{N\sqrt{3}}{3}$

Cube this sidelength to get the volume:

$s^{3} = \left ( \frac{N\sqrt{3}}{3} \right )^{3} = \frac{N^{3} \left ( \sqrt{3}\right ) ^{3} }{3^{3} } = \frac{N^{3} \left (3 \sqrt{3}\right ) }{27 }= \frac{N^{3} \sqrt{3} }{9 }$

Report an Error

Example Question #2 : How To Find The Volume Of A Cube

Give the volume of a cube with surface area .

Possible Answers:

$\frac{N\sqrt{ 6N} }{36}$

$6\sqrt[3]{N^{2}}$

$\frac{N^{3}}{36}$

$6N\sqrt{ 6N}$

$\frac{N^{3}}{216}$

Correct answer:

$\frac{N\sqrt{ 6N} }{36}$

Explanation:

Let be the length of one edge of the cube. Since its surface area is , one face has one-sixth of this area, or $\frac{N}{6}$ . Therefore,

$s^{2} = \frac{N}{6}$ ,

and

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

Cube this sidelength to get the volume:

$s ^{3}= \left ( \frac{ \sqrt{ 6N}}{6} \right )^{3} = \frac{\left ( \sqrt{ 6N} \right )^{3}}{6^{3}}= \frac{ 6N\sqrt{ 6N} }{216}= \frac{N\sqrt{ 6N} }{36}$

Report an Error

Example Question #5 : How To Find The Volume Of A Cube

The length of a diagonal of one face of a cube is 10. Give the volume of the cube.

Possible Answers:

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

$500\sqrt{2}$

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

$250\sqrt{2}$

$125\sqrt{2}$

Correct answer:

$250\sqrt{2}$

Explanation:

Since a diagonal of a square face of the cube is 10, each side of each square has length $\frac{\sqrt{2}}{2}$ times this, or $10 \cdot \frac{\sqrt{2}}{2} = 5\sqrt{2}$ .

Cube this to get the volume of the cube:

$\left (5\sqrt{2} \right )^{3}= 5^{3} \left ( \sqrt{2} \right )^{3} = 125 \left (2 \sqrt{2} \right ) = 250 \sqrt{2}$ .

Report an Error

Example Question #3 : How To Find The Volume Of A Figure

An aquarium is shaped like a perfect cube; the area of each glass face is 1.44 square meters. If it is filled to the recommended 90% capacity, then, to the nearest hundred liters, how much water will it contain?

Note: 1 cubic meter = 1,000 liters.

Possible Answers:

$1,300\textup{ L}$

$1,700\textup{ L}$

$1,200\textup{ L}$

$1,600 \textup{ L}$

$1,400\textup{ L}$

Correct answer:

$1,600 \textup{ L}$

Explanation:

A perfect cube has square faces; if a face has area 1.44 square meters, then each side of each face measures the square root of this, or 1.2 meters. The volume of the tank is the cube of this, or

$1.2^{3} = 1.728$ cubic meters.

Its capacity in liters is $1.728 \times 1,000 = 1,728$ liters.

90% of this is

$1,728 \times 0.9 = 1,555.2$ liters.

This rounds to 1,600 liters, the correct response.

Report an Error

Example Question #3 : How To Find The Volume Of A Cube

Give the volume of a cube with surface area 3 square meters.

Possible Answers:

$250,000 \textup{ cm}^{3}$

$125,000\sqrt{3} \textup{ cm}^{3}$

$250,000\sqrt{2} \textup{ cm}^{3}$

$125,000 \textup{ cm}^{3}$

$125,000\sqrt{2} \textup{ cm}^{3}$

Correct answer:

$250,000\sqrt{2} \textup{ cm}^{3}$

Explanation:

Let be the length of one edge of the cube. Since its surface area is 3 square meters, one face has one-sixth of this area, or $\frac{3}{6} = \frac{1}{2}$ square meters. Therefore, $s^{2} = \frac{1}{2}$ , and $s = \sqrt{ \frac{1}{2}} = \frac{\sqrt{1}}{\sqrt{2}}=\frac{1 \cdot \sqrt{2}}{\sqrt{2}\cdot \sqrt{2}}= \frac{\sqrt{2}}{2}$ meters.

The choices are in centimeters, so multiply this by 100 - the sidelength is

$\frac{\sqrt{2}}{2} \cdot 100 = 50 \sqrt{2}$ centimeters.

The volume is the cube of this, or $V= \left ( 50 \sqrt{2} \right )^{3}= 50^{3} \cdot \left ( \sqrt{2} \right )^{3}= 125,000 \cdot 2 \sqrt{2}= 250,000\sqrt{2}$ cubic centimeters.

Report an Error

Example Question #7 : How To Find The Volume Of A Cube

The length of a diagonal of a cube is $15\sqrt{2}$ . Give the volume of the cube.

Possible Answers:

$750 \sqrt{2}$

$750 \sqrt{6}$

$1,500 \sqrt{2}$

$750 \sqrt{3}$

$1,500 \sqrt{3}$

Correct answer:

$750 \sqrt{6}$

Explanation:

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

$s^{2}+s^{2}+s^{2}= (15 \sqrt{2})^{2}$

$3s^{2}=15 ^{2}\cdot \left ( \sqrt{2} \right )^{2}$

$3s^{2}=225 \cdot 2 = 450$

$s^{2} = 150$

$s = \sqrt{150 } = \sqrt{25} \cdot \sqrt{6} = 5\sqrt{6}$

Cube the sidelength to get the volume:

$s ^{3 }= \left ( 5\sqrt{6} \right )^{3 }$

$s ^{3 }= 5^{3 } \left (\sqrt{6} \right )^{3 } = 125 \cdot 6 \sqrt{6} = 750 \sqrt{6}$

Report an Error

Example Question #3 : How To Find The Volume Of A Cube

The length of a diagonal of one face of a cube is $16\sqrt{2}$ . Give the volume of the cube.

Possible Answers:

$8,192\sqrt{2}$

$65,536\sqrt{2}$

32,768

4,096

The correct answer is not among the other responses.

Correct answer:

4,096

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 $16 \sqrt{2} \div \sqrt{2}= 16$ . Cube this to get the volume:

$16^{3} = 4,096$

Report an Error

View SSAT- Upper Level Tutors

Laura Jeanne
Certified Tutor

Texas Tech University, Bachelor in Arts, Music Teacher Education. Asbury Theological Seminary, Master of Divinity, Music Teac...

View SSAT- Upper Level Tutors

Keith
Certified Tutor

Xavier University, Bachelor in Business Administration, Accounting. Ohio University-Main Campus, Masters in Education, Mathem...

View SSAT- Upper Level Tutors

Zander
Certified Tutor

Rowan-Cabarrus Community College, Associate in Arts, General Studies. North Carolina State University at Raleigh, Bachelor of...

All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

LSAT Tutors in Houston, Statistics Tutors in Houston, Calculus Tutors in Boston, ISEE Tutors in New York City, Statistics Tutors in Boston, French Tutors in Philadelphia, Computer Science Tutors in Boston, Reading Tutors in Denver, GRE Tutors in Boston, Computer Science Tutors in Dallas Fort Worth

Popular Courses & Classes

MCAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Chicago, SAT Courses & Classes in Houston, MCAT Courses & Classes in New York City, GMAT Courses & Classes in Boston, GMAT Courses & Classes in Washington DC, LSAT Courses & Classes in Miami, GRE Courses & Classes in Boston, ACT Courses & Classes in Philadelphia, Spanish Courses & Classes in Washington DC

Popular Test Prep

GMAT Test Prep in San Diego, ACT Test Prep in Washington DC, LSAT Test Prep in Atlanta, SSAT Test Prep in Los Angeles, GRE Test Prep in San Francisco-Bay Area, ACT Test Prep in Philadelphia, SAT Test Prep in Los Angeles, LSAT Test Prep in Boston, GMAT Test Prep in Washington DC, GMAT Test Prep in Los Angeles

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)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

SSAT Upper Level Math : How to find the volume of a cube

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #1 : How To Find The Volume Of A Cube

Example Question #1 : How To Find The Volume Of A Cube

Example Question #2 : How To Find The Volume Of A Figure

Example Question #4 : How To Find The Volume Of A Cube

Example Question #2 : How To Find The Volume Of A Cube

Example Question #5 : How To Find The Volume Of A Cube

Example Question #3 : How To Find The Volume Of A Figure

Example Question #3 : How To Find The Volume Of A Cube

Example Question #7 : How To Find The Volume Of A Cube

Example Question #3 : How To Find The Volume Of A Cube

All SSAT Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: