We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : How to find the volume of a cube

Study concepts, example questions & explanations for Intermediate Geometry

Create An Account

All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 Next →

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

A cube has edges that are three times as long as those of a smaller cube. The volume of the bigger cube is how many times larger than that of the smaller cube?

Possible Answers:

Correct answer:

Explanation:

If we let represent the length of an edge on the smaller cube, its volume is $x^{3}$ .

The larger cube has edges three times as long, so the length can be represented as . The volume is $(3x)^{3}$ , which is $27x^{3}$ .

The large cube's volume of $27x^{3}$ is 27 times as large as the small cube's volume of $x^{3}$ .

Report an Error

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

The side length of a cube is inches.

What is the volume?

Possible Answers:

$294\, in^2$

$7\, in^3$

$343\,in^3$

$21 \, in^3$

Correct answer:

$343\,in^3$

Explanation:

The volume of a cube is

V = s^3

So with a side length of 7 inches, the volume is

$V = 7^{3}\, in^3 = 343\, in^3$

Report an Error

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

The side length of a cube is ft.

What is the volume?

Possible Answers:

$24\, ft^2$

$8\,ft^3$

$4\, ft^3$

$6\, ft^3$

Correct answer:

$8\,ft^3$

Explanation:

The volume of a cube is

V = s^3

So with a side length of 2 ft, the volume is

$V = 2^{3}\, ft^3 = 8\, ft^3$

Report an Error

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

Find the volume of a cube with an edge length of $7\:in$ .

Possible Answers:

$294\:in^3$

$308\:in^3$

$252\:in^3$

$49\:in^3$

$343\:in^3$

Correct answer:

$343\:in^3$

Explanation:

The volume of a cube can be determined through the equation V = s^3 , where stands for the length of one side of the cube. The equation is $s\cdot s\cdot s$ because all edges in a cube are the same length. The value for the given edge just needs to be substituted into the equation for in order to solve for the cube's volume.

V = s^3

V = 7^3

$V = 7 \cdot 7\cdot 7$

$V = 343\:in^3$

Report an Error

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

If the side of a cube is $1\:m$ in length, what is the volume of the cube?

Possible Answers:

$4\:m^3$

$2\:m^3$

$1\:m^3$

$3\:m^3$

$6\:m^3$

Correct answer:

$1\:m^3$

Explanation:

To find the volume of a cube we just multiply a length of one of the cube's sides by itself three times, or in other words, cube it. If we call the length of a side of a cube , then:

Volume=a^3

The side of our cube is $1\:m$ in length, so we can substitute this into the equation and solve:

$Volume=a^3=(1\:m)^3=1\:m^3$

Report an Error

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

A Rubik's Cube is made up of three square layers, with nine identical smaller cubes in each layer. If one of the smaller cubes has side lenghts of 1.5 cm, what is the approximate volume of a whole Rubik's Cube?

Possible Answers:

$3.375 \; cm^3$

$91.125 \; cm^3$

$40.5 \; cm^3$

$13.5 \; cm^3$

$30.375 \; cm^3$

Correct answer:

$91.125 \; cm^3$

Explanation:

This is a great problem becaue ther are two ways to approach it. The simplest way is to realize that because each edge of the Rubik's Cube is made up of 3 of the smaller cubes we can find the edge length for the whole Rubik's Cube:

1.5 cm + 1.5 cm + 1.5 cm = 4.5 cm (edge of whole Rubik's Cube)

Now that we know the edge length finding the volume is easy, we simply multiply the length, width, and height of the cube to find the volume. This is easy because the length, width, and height are all 4.5 cm.

$4.5 \; cm \times 4.5 \; cm \times 4.5 \; cm = 91.125 \; cm^3$ (vol. of Rubik's Cube)

This is the answer. Another way to approach the problem would be by finding the volume of one of the smaller cubes, then multiplying by 9 to find the volume of one layer, then multiplying by three, because there are 3 layers.

$1.5 \; cm \times 1.5 \; cm \times 1.5 \; cm = 3.375\; cm^3$ (vol. of one small cube)

$3.375 \; cm^3 \times 9 = 30.375 \;cm^3$ (vol. of one layer of Rubik's Cube)

$30.375 \; cm^3 \times 3 = 91.125 \; cm^3$ (vol. of Rubik's Cube)

Two different methods and we got the same answer!

Report an Error

Example Question #6 : How To Find The Volume Of A Cube

A cylinder is cut out of a cube as shown by the figure below.

Find the volume of the figure.

Possible Answers:

215.20

290.03

274.11

285.81

Correct answer:

285.81

Explanation:

In order to find the volume of the figure, we must first find the volumes of the cube and the cylinder.

Recall how to find the volume of a cube.

$\text{Volume of Cube}=\text{side}^3$

Plug in the given side length of the cube to find the volume.

$\text{Volume of Cube}=8^3=512$

Next, recall how to find the volume of a cylinder.

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Use the given diameter to find the length of the radius.

$\text{Radius}=\frac{\text{Diameter}}{2}=\frac{6}{2}=3$

Find the volume of the cylinder.

$\text{Volume of Cylinder}=\pi\times 3^2 \times 8=72\pi$

To find the volume of the figure, subtract the volume of the cylinder from the volume of the cube.

$\text{Volume of Figure}=512-72\pi=285.81$

Make sure to round to places after the decimal.

Report an Error

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

A cylinder is cut out of a cube as shown by the figure below.

Find the volume of the figure.

Possible Answers:

803.65

852.24

792.08

750.22

Correct answer:

803.65

Explanation:

In order to find the volume of the figure, we must first find the volumes of the cube and the cylinder.

Recall how to find the volume of a cube.

$\text{Volume of Cube}=\text{side}^3$

Plug in the given side length of the cube to find the volume.

$\text{Volume of Cube}=10^3=1000$

Next, recall how to find the volume of a cylinder.

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Use the given diameter to find the length of the radius.

$\text{Radius}=\frac{\text{Diameter}}{2}=\frac{5}{2}=2.5$

Find the volume of the cylinder.

$\text{Volume of Cylinder}=\pi\times 2.5^2 \times 10=62.5\pi$

To find the volume of the figure, subtract the volume of the cylinder from the volume of the cube.

$\text{Volume of Figure}=1000-62.5\pi=803.65$

Make sure to round to places after the decimal.

Report an Error

Example Question #8 : How To Find The Volume Of A Cube

A cylinder is cut out of a cube as shown by the figure below.

Find the volume of the figure.

Possible Answers:

1447.22

1236.30

1080.69

1124.81

Correct answer:

1124.81

Explanation:

In order to find the volume of the figure, we must first find the volumes of the cube and the cylinder.

Recall how to find the volume of a cube.

$\text{Volume of Cube}=\text{side}^3$

Plug in the given side length of the cube to find the volume.

$\text{Volume of Cube}=12^3=1728$

Next, recall how to find the volume of a cylinder.

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Use the given diameter to find the length of the radius.

$\text{Radius}=\frac{\text{Diameter}}{2}=\frac{8}{2}=4$

Find the volume of the cylinder.

$\text{Volume of Cylinder}=\pi\times 4^2 \times 12=192\pi$

To find the volume of the figure, subtract the volume of the cylinder from the volume of the cube.

$\text{Volume of Figure}=1728-192\pi=1124.81$

Make sure to round to places after the decimal.

Report an Error

Example Question #9 : How To Find The Volume Of A Cube

A cylinder is cut out of a cube as shown by the figure below.

Find the volume of the figure.

Possible Answers:

92.51

102.49

84.45

89.66

Correct answer:

89.66

Explanation:

In order to find the volume of the figure, we must first find the volumes of the cube and the cylinder.

Recall how to find the volume of a cube.

$\text{Volume of Cube}=\text{side}^3$

Plug in the given side length of the cube to find the volume.

$\text{Volume of Cube}=5^3=125$

Next, recall how to find the volume of a cylinder.

$\text{Volume of Cylinder}=\pi\times\text{radius}^2\times\text{height}$

Use the given diameter to find the length of the radius.

$\text{Radius}=\frac{\text{Diameter}}{2}=\frac{3}{2}=1.5$

Find the volume of the cylinder.

$\text{Volume of Cylinder}=\pi\times 1.5^2 \times 5=11.25\pi$

To find the volume of the figure, subtract the volume of the cylinder from the volume of the cube.

$\text{Volume of Figure}=125-11.25\pi=89.66$

Make sure to round to places after the decimal.

Report an Error

← Previous 1 2 3 4 Next →

View Tutors

Stanley
Certified Tutor

University of Pennsylvania, Bachelor in Arts, History.

View Tutors

Matthew
Certified Tutor

Rider University, Bachelor of Science, Chemistry. Rutgers University-Camden, Master of Science, Organic Chemistry.

View Tutors

Erik
Certified Tutor

University of Illinois at Urbana-Champaign, Bachelor of Science, Physics. University of California-San Diego, Master of Scien...

All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Math Tutors in Boston, Reading Tutors in Seattle, ISEE Tutors in Boston, Reading Tutors in Phoenix, Biology Tutors in San Francisco-Bay Area, ACT Tutors in Phoenix, Math Tutors in Philadelphia, French Tutors in Boston, Computer Science Tutors in San Francisco-Bay Area, Math Tutors in Chicago

Popular Courses & Classes

Spanish Courses & Classes in Phoenix, SAT Courses & Classes in Denver, SSAT Courses & Classes in Atlanta, SSAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Boston, LSAT Courses & Classes in Seattle, LSAT Courses & Classes in Phoenix, GMAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Miami, ACT Courses & Classes in Washington DC

Popular Test Prep

MCAT Test Prep in Chicago, MCAT Test Prep in Phoenix, SSAT Test Prep in New York City, ACT Test Prep in Miami, MCAT Test Prep in Denver, ACT Test Prep in Washington DC, MCAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Philadelphia, ISEE Test Prep in Atlanta, GRE Test Prep in San Diego

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

Intermediate Geometry : How to find the volume of a cube

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry 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 Cube

Example Question #3 : 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 #6 : How To Find The Volume Of A Cube

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

Example Question #8 : How To Find The Volume Of A Cube

Example Question #9 : How To Find The Volume Of A Cube

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: