We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

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

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

Create An Account

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Cubes

If a cube is inches tall, what is its volume?

Possible Answers:

Not enough information provided.

512

500

384

Correct answer:

512

Explanation:

To find the volume of a cube, we multiply length by width by height, which can be represented with the forumla $v=l\cdot w\cdot h$ . Since a cube has equal sides, we can use for all three values.

$8\cdot 8\cdot 8=512\: in ^{3}$

Report an Error

Example Question #1 : Volume Of A Rectangular Solid

What is the volume of a cube with a side length equal to inches?

Possible Answers:

$343\: in^{3}$

$21\: in^{3}$

$49\: in^{3}$

$53\: in^{3}$

Correct answer:

$343\: in^{3}$

Explanation:

The volume of a a cube (or rectangular prism) can be solved using the following equation:

$V=l\times\ w\times\ h$

$V=7in\times 7in\times 7in=343in^3$

Report an Error

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

Give the volume of a cube with surface area 150 square inches.

Possible Answers:

$125\sqrt{3}\textup{ in}^{3}$

$125\textup{ in}^{3}$

$250\sqrt{3}\textup{ in}^{3}$

$250\textup{ in}^{3}$

$375\textup{ in}^{3}$

Correct answer:

$125\textup{ in}^{3}$

Explanation:

Let be the length of one edge of the cube. Since its surface area is 150 square inches, one face has one-sixth of this area, or $\frac{150}{6} = 25$ square inches. Therefore, $s^{2} = 25$ , and s = 5 .

The volume is the cube of this, or $V= 5^{3}=125$ cubic inches.

Report an Error

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

What is the volume of a cube in which the edge is equal to $\sqrt[3]{x}$ , and the value of is:

$x=5(4+3^{2})-3$

Possible Answers:

Correct answer:

Explanation:

First, the value of x must be solved for:

$x=5(4+3^{2})-3$

x=5(4+9)-3

x=5(13)-3

x=62

Given the edge of the cube is $\sqrt[3]{x}$ , plugging in the value of x results in $\sqrt[3]{62}$ . Thus, the area would be equal to this value cubed, which would result in 62.

Thus, 62 is the correct answer.

Report an Error

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

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

Possible Answers:

$3N^{3}$

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

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

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

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

Correct answer:

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

Explanation:

Since a diagonal of a square face of the cube is, each side of each square has length $\frac{N}{\sqrt{2}}=\frac{N\sqrt{2}}{2}$ .

Cube this to get the volume of the cube:

$\left (\frac{N\sqrt{2}}{2} \right )^{3}$

$= \frac{N^{3}\left ( \sqrt{2} \right )^{3} }{2^{3} }$

$= \frac{N^{3} \cdot 2 \sqrt{2} }{8}$

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

Report an Error

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

The distance from one vertex of a perfectly cubic aquarium to its opposite vertex is 1.5 meters. Give the volume of the aquarium in liters.

1 cubic meter = 1,000 liters.

Possible Answers:

$843\frac{3}{4} \textup{ L}$

The correct answer is not given among the other responses.

$375 \textup{ L}$

$750\textup{ L}$

$421\frac{7}{8} \textup{ L}$

Correct answer:

The correct answer is not given among the other responses.

Explanation:

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

$s^{2}+s^{2}+s^{2}=1.5^{2}$

$3s^{2}=2.25$

$s^{2} = 0.75 = \frac{3}{4}$

$s = \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{\sqrt{4}}} = \frac{\sqrt{3}}{2}$ meters.

Cube this sidelength to get the volume:

$s ^{3 } =\left ( \frac{\sqrt{3}}{2} \right )^{3 }= \frac{\left (\sqrt{3}\right )^{3 }}{2^{3 } } = \frac{ 3\sqrt{3} }{8 }$ cubic meters.

To convert this to liters, multiply by 1,000:

$\frac{ 3\sqrt{3} }{8 } \cdot 1,000 = \frac{ 3\sqrt{3} }{8 } \cdot \frac{1,000}{1} = \frac{ 3\sqrt{3} }{1 } \cdot \frac{125}{1}= 375\sqrt{3}$ liters.

This is not among the given responses.

Report an Error

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

Give the volume of a cube with surface area 240 square inches.

Possible Answers:

$80 \textup{ in}^{3}$

$40 \sqrt{10} \textup{ in}^{3}$

$120 \textup{ in}^{3}$

$80 \sqrt{10} \textup{ in}^{3}$

$120 \sqrt{10} \textup{ in}^{3}$

Correct answer:

$80 \sqrt{10} \textup{ in}^{3}$

Explanation:

Let be the length of one edge of the cube. Since its surface area is 240 square inches, one face has one-sixth of this area, or $\frac{240}{6} = 40$ square inches. Therefore, $s^{2} = 40$ , and $s = \sqrt{40} = 2\sqrt{10}$ .

The volume is the cube of this, or $V= \left ( 2\sqrt{10} \right )^{3}= 2^{3} \cdot \left ( \sqrt{10} \right )^{3}= 8 \cdot 10 \sqrt{10}= 80 \sqrt{10}$ cubic inches.

Report an Error

Example Question #1 : Finding Volume Of A Rectangular Prism

An aquarium is shaped like a perfect cube; the perimeter of each glass face is 8.4 meters. If it is filled to the recommended $90\%$ capacity, then, to the nearest hundred cubic liters, how much water will it contain?

Possible Answers:

Insufficient information is given to answer the question.

$4\textup,400\textup{ L}$

$4\textup,000\textup{ L}$

$8\textup,300\textup{ L}$

$9\textup,300\textup{ L}$

Note: $1\textup{ cubic meter}= 1\textup{,}000\textup{ cubic liters}$

Correct answer:

$8\textup,300\textup{ L}$

Explanation:

A perfect cube has square faces; if a face has perimeter 8.4 meters, then each side of each face measures one fourth of this, or 2.1 meters. The volume of the tank is the cube of this, or

$2.1^{3} = 9.261$ cubic meters.

Its capacity in liters is $9.261 \times 1,000 = 9,261$ liters.

$90\%$ of this is

$9,261 \times 0.9 = 8,335$ liters.

This rounds to $8\textup,300$ liters, the correct response.

Report an Error

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

Your friend gives you a puzzle cube for your birthday. If the length of one edge is 5cm, what is the volume of the cube?

Possible Answers:

15cm^3

625cm^3

125cm^3

25cm^3

Correct answer:

125cm^3

Explanation:

Your friend gives you a puzzle cube for your birthday. If the length of one edge is 5cm, what is the volume of the cube?

To find the volume of a cube, use the following formula:

$V_{cube}=s^3$

Where s is the side length.

Plug in what we know to get our answer:

V=(5cm)^3=125cm^3

Report an Error

Example Question #4 : Cubes

A cube has a side length of 9 mm , what is the volume of the cube?

Possible Answers:

486mm^3

81mm^3

72.9mm^3

729mm^3

Correct answer:

729mm^3

Explanation:

A cube has a side length of 9 mm , what is the volume of the cube?

To find the volume of a cube, use the following formula:

$V_{cube}=s^3$

Plug in our known side length and solve

$V_{cube}=(9mm)^3=729mm^3$

Making our answer:

729mm^3

Report an Error

View Tutors

Pavan
Certified Tutor

University of Tennessee, Knoxville, Master's/Graduate, Mechanical Engineering. Pennsylvania State University, Master's/Gradua...

View Tutors

Omar
Certified Tutor

Arizona State University, Bachelors, Civil Engineering.

View Tutors

Ana
Certified Tutor

Grand Canyon University, Bachelors, Education. Grand Canyon University, Masters, Education.

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in Houston, English Tutors in Chicago, MCAT Tutors in New York City, GRE Tutors in New York City, ISEE Tutors in San Diego, English Tutors in Atlanta, French Tutors in Dallas Fort Worth, Chemistry Tutors in San Francisco-Bay Area, French Tutors in Phoenix, SSAT Tutors in San Diego

Popular Courses & Classes

MCAT Courses & Classes in Los Angeles, SSAT Courses & Classes in Boston, ACT Courses & Classes in Denver, Spanish Courses & Classes in Phoenix, ISEE Courses & Classes in Chicago, Spanish Courses & Classes in Chicago, GMAT Courses & Classes in Los Angeles, Spanish Courses & Classes in Boston, ACT Courses & Classes in Boston, MCAT Courses & Classes in Denver

Popular Test Prep

LSAT Test Prep in Washington DC, SAT Test Prep in Seattle, GMAT Test Prep in Phoenix, ACT Test Prep in Boston, MCAT Test Prep in Miami, SAT Test Prep in Chicago, SAT Test Prep in Boston, LSAT Test Prep in Boston, GRE Test Prep in San Diego, LSAT Test Prep in Phoenix

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

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

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 : Cubes

Example Question #1 : Volume Of A Rectangular Solid

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

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 Cube

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

Example Question #1 : Finding Volume Of A Rectangular Prism

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

Example Question #4 : Cubes

All ISEE Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: