We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Solid Geometry

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 6 7 8 9 10 11 … 15 16 Next →

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

A cube has a surface area of 294 units squared. What is its volume?

Possible Answers:

216 units cubed

729 units cubed

512 units cubed

343 units cubed

Correct answer:

343 units cubed

Explanation:

Since a cube has square faces and the surface area of each face is given by multiplying the length of one side of the square face by itself, the equation for the surface area of a cube is A = 6s^2 , where is the length of one side of one face (i.e., one edge of the cube). Find the length of one side/edge of the given cube by setting the given surface area equal to 6s^2 :

6s^2 = 294

$\rightarrow s^2 = 49$

$\rightarrow s = 7$ units

The volume of a cube is s^3 , where is the length of one of the cube's edges. Substituing the solution to the previous equation for in the volume equation gives the volume of the cube:

V = s^3

$\rightarrow V = (7)^3$

$\rightarrow V = 343$ units cubed

Report an Error

Example Question #11 : How To Find The Volume Of A Cube

Find the volume of the following cube:

Length_of_diagonal

Possible Answers:

$68\ m^3$

$56\ m^3$

$60\ m^3$

$52\ m^3$

$64\ m^3$

Correct answer:

$64\ m^3$

Explanation:

The formula for the volume of a cube is

V=(s)^3 ,

where is the side of the cube.

Plugging in our values, we get:

$V=(4\ m)^3$

$V=64\ m^3$

Report an Error

Example Question #12 : How To Find The Volume Of A Cube

What is the difference in volume between a sphere with radius x and a cube with a side of 2x? Let π = 3.14

Possible Answers:

4.18x³

5.28x³

6.73x³

3.82x³

8.00x³

Correct answer:

3.82x³

Explanation:

V_cube = s³ = (2x)³ = 8x³

V_sphere = 4/3 πr³ = 4/3•3.14•x³ = 4.18x³

Report an Error

Example Question #13 : How To Find The Volume Of A Cube

The density of gold is $16\ g/cm^3$ and the density of glass is $2\ g/cm^3$ . You have a gold cube that is $x\ cm$ in length on each side. If you want to make a glass cube that is the same weight as the gold cube, how long must each side of the glass cube be?

Possible Answers:

2.5x

1.5x

Correct answer:

Explanation:

Weight = Density * Volume

Volume of Gold Cube = side³= x³

Weight of Gold = 16 g/cm³* x³

Weight of Glass = 3/cm³ * side³

Set the weight of the gold equal to the weight of the glass and solve for the side length:

16* x³ = 2 * side³

side³ = 16/2* x³= 8 x³

Take the cube root of both sides:

side = 2x

Report an Error

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 #15 : How To Find The Volume Of A Cube

If a cube has its edges increased by a factor of 5, what is the ratio of the new volume to the old volume?

Possible Answers:

125:1

25:1

100:1

5:1

15:1

Correct answer:

125:1

Explanation:

A cubic volume is side*side*side . Let the original sides be 1, so that the original volume is 1. Then find the volume if the sides measure 5. This new volume is 125. Therefore, the ratio of new volume to old volume is 125: 1.

Report an Error

Example Question #16 : How To Find The Volume Of A Cube

A cube has a side length of meters. What is the volume of the cube?

Possible Answers:

$6\ \textup{m}^{3}$

$16\ \textup{m}^{3}$

$4\ \textup{m}^{3}$

$2\ \textup{m}^{3}$

$8\ \textup{m}^{3}$

Correct answer:

$8\ \textup{m}^{3}$

Explanation:

The formula for the volume of a cube is:

$Volume = (side)^{3}$

Since the length of one side is meters, the volume of the cube is:

$2^{3 } = 8$ meters cubed.

Report an Error

Example Question #17 : How To Find The Volume Of A Cube

If the length of the side of a cube is $8x^{2}$ , which expression represents the volume of the cube?

Possible Answers:

none of the other answers

$512x^{3}$

$64x^{6}$

$512x^{6}$

$8x^{3}$

Correct answer:

$512x^{6}$

Explanation:

The formula for the volume of the cube is $V = x^{3}$

Plugging that into Volume equation, we find $8^{3}$ and $(x^{^{2)^{3}}}$

Thus, the answer is 512x⁶

Report an Error

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

A tank measuring 3in wide by 5in deep is 10in tall. If there are two cubes with 2in sides in the tank, how much water is needed to fill it?

Possible Answers:

150 in^3

8 in^3

160 in^3

134 in^3

16 in^3

Correct answer:

134 in^3

Explanation:

$Volume_{Tank} = Width \cdot Depth \cdot Height$

$Volume_{Tank} = 3in \cdot 5in \cdot 10in = 150 in^3$

$Volume_{Cube} = (Side)^3 = (2in)^3 = 8 in^3$

$Volume_{Water}=Volume_{Tank}-2(Volume_{Cube})$

$Volume_{Water}=150-2(8)$

$Voume_{Water}=150-16$

$Volume_{Water}=134in^3$

Report an Error

Example Question #1 : Pyramids

What is the volume of a pyramid with a height of and a square base with a side length of ?

Possible Answers:

105

245

175

285

Correct answer:

245

Explanation:

To find the volume of a pyramid we must use the equation

$Volume\: of\: pyramid=\frac{1}{3}(area\ of\ base)(height)$

We must first solve for the area of the square using

$A=(side\ length^{2})$

We plug in and square it to get A=49

We then plug our answer into the equation for the pyramid with the height to get

$V=\frac{1}{3}(49)(15)$

We multiply the result to get our final answer for the volume of the pyramid

V=245 .

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 10 11 … 15 16 Next →

View Tutors

Katrina
Certified Tutor

Montclair State University, Bachelor in Arts, Psychology. New Jersey City University, Bachelor of Science, Early Childhood Ed...

View Tutors

Aaron
Certified Tutor

Austin Peay State University, Bachelor, Education.

View Tutors

Yucheng
Certified Tutor

The University of Texas at Austin, Bachelor of Science, Mechanical Engineering.

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

SAT Tutors in Seattle, Math Tutors in Los Angeles, SSAT Tutors in Seattle, GRE Tutors in Houston, English Tutors in Philadelphia, MCAT Tutors in Denver, Statistics Tutors in San Diego, Physics Tutors in Chicago, Calculus Tutors in Los Angeles, Spanish Tutors in Chicago

Popular Courses & Classes

LSAT Courses & Classes in Houston, LSAT Courses & Classes in Boston, GRE Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Seattle, SAT Courses & Classes in Chicago, Spanish Courses & Classes in Seattle, GMAT Courses & Classes in Denver, ISEE Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Atlanta, SSAT Courses & Classes in Miami

Popular Test Prep

GMAT Test Prep in Atlanta, ISEE Test Prep in Philadelphia, MCAT Test Prep in Dallas Fort Worth, LSAT Test Prep in New York City, MCAT Test Prep in Seattle, LSAT Test Prep in Denver, ACT Test Prep in Los Angeles, GRE Test Prep in Denver, ISEE Test Prep in Denver, LSAT Test Prep in Miami

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

High School Math : Solid Geometry

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

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

Example Question #11 : How To Find The Volume Of A Cube

Example Question #12 : How To Find The Volume Of A Cube

Example Question #13 : How To Find The Volume Of A Cube

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

Example Question #15 : How To Find The Volume Of A Cube

Example Question #16 : How To Find The Volume Of A Cube

Example Question #17 : How To Find The Volume Of A Cube

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

Example Question #1 : Pyramids

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: