Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Math : Solid Geometry

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 #51 : Solid Geometry

Find the surface area of a cube with a width of 7in.

Possible Answers:

$294\text{in}^2$

$84\text{in}^2$

$147\text{in}^2$

$245\text{in}^2$

$343\text{in}^2$

Correct answer:

$294\text{in}^2$

Explanation:

To find the surface area of a cube, we will use the following formula.

SA = 6a^2

where a is the length of any side of the cube.

Now, we know the width of the cube is 7in. Because it is a cube, all sides are equal (this is why we can use any length in the formula). So, we will use 7in in the formula. We get

$SA = 6 \cdot (7\text{in})^2$

$SA = 6 \cdot 49\text{in}^2$

$SA = 294\text{in}^2$

Report an Error

Example Question #51 : Solid Geometry

Find the surface area of a cube with a width of 6in.

Possible Answers:

$72\text{in}^2$

$27\text{in}^2$

$432\text{in}^2$

$216\text{in}^2$

$144\text{in}^2$

Correct answer:

$216\text{in}^2$

Explanation:

To find the surface area of a cube, we will use the following formula:

$SA = 6 \cdot l \cdot w$

where l is the length, and w is the width of the cube.

Now, we know the width of the cube is 6in. Because it is a cube, all lengths, widths, and heights are the same. Therefore, the length is also 6in.

Knowing this, we can substitute into the formula. We get

$SA = 6 \cdot 6\text{in} \cdot 6\text{in}$

$SA = 6 \cdot 36\text{in}^2$

$SA = 216\text{in}^2$

Report an Error

Example Question #52 : Solid Geometry

Find the surface area of a cube with a length of 9cm.

Possible Answers:

$338\text{cm}^2$

$576\text{cm}^2$

$486\text{cm}^2$

$324\text{cm}^2$

$218\text{cm}^2$

Correct answer:

$486\text{cm}^2$

Explanation:

To find the surface area of a cube, we will use the following formula:

SA = 6 a^2

where a is the length of one side of the cube.

Now, we know the length of the cube is 9cm. So, we get

$SA = 6 \cdot (9\text{cm})^2$

$SA = 6 \cdot 81\text{cm}^2$

$SA = 486\text{cm}^2$

Report an Error

Example Question #52 : Solid Geometry

Find the surface area of a cube with a width of 6cm.

Possible Answers:

$428\text{cm}^2$

$96\text{cm}^2$

$216\text{cm}^2$

$128\text{cm}^2$

$361\text{cm}^2$

Correct answer:

$216\text{cm}^2$

Explanation:

To find the surface area of a cube, we will use the following formula.

SA = 6a^2

where a is the length of any side of the cube.

Now, we know the width of the cube is 6cm.

So, we get

$SA = 6 \cdot (6\text{cm})^2$

$SA = 6 \cdot 6\text{cm}^2$

$SA = 216\text{cm}^2$

Report an Error

Example Question #2 : Volume Of A Rectangular Solid

The volume of a cube is . What is the length of an edge of the cube?

Possible Answers:

Correct answer:

Explanation:

Let be the length of an edge of the cube. The volume of a cube can be determined by the equation:
x^3=V

x^3=64

$\sqrt[3]{x^3}=\sqrt[3]{64}$

x=4

Report an Error

Example Question #52 : Solid Geometry

There is a sculpture in front of town hall which is shaped like a cube. If it has a volume of , what is the length of one side of the cube?

Possible Answers:

7ft

14ft

49ft^2

49ft

Correct answer:

7ft

Explanation:

There is a sculpture in front of town hall which is shaped like a cube. If it has a volume of , what is the length of one side of the cube?

To find the side length of a cube from its volume, simply use the following formula:

$V_{cube}=s^3$

Plug in what is known and use some algebra to get our answer:

$s=\sqrt[3]{343ft^3}=7ft$

Report an Error

Example Question #1 : How To Find The Length Of An Edge Of A Cube

You have a cube with a volume of 125 m^3 . What is the cube's side length?

Possible Answers:

25m

10m

15m

Correct answer:

Explanation:

You have a cube with a volume of 125 m^3 . What is the cube's side length?

If we begin with the formula for volume of a cube, we can work backwards to find the side length.

$V_{cube}=s^3$

125m^3=s^3

$s=\sqrt[3]{125m^3}=5m$

Making our answer:

Report an Error

Example Question #371 : Geometry

Cube

The above cube has surface area 486. Evaluate .

Possible Answers:

x = 63

x =2

x = 9

x = 16

Correct answer:

x = 16

Explanation:

The surface area of a cube is six times the square of the length of each edge, which here is x- 7 . Therefore,

$6s^{2} = A$

Substituting, then solving for :

$6 (x-7)^{2} = 486$

$6 (x-7)^{2} \div 6 = 486 \div 6$

$(x-7)^{2} = 81$

$\sqrt{(x-7)^{2} }= \sqrt{81}$

Since the sidelength is positive,

x- 7 = 9

x = 16

Report an Error

Example Question #2 : How To Find The Length Of An Edge Of A Cube

You have a crate with equal dimensions (height, length and width). If the volume of the cube is 216 m^3 , what is the length of one of the crate's dimension?

Possible Answers:

Not enough information to solve the equation.

6 m

36m

12 m

Correct answer:

6 m

Explanation:

You have a crate with equal dimensions (height, length and width). If the volume of the cube is 216 m^3 , what is the length of one of the crate's dimension?

Let's begin with realizing that we are dealing with a cube. A crate with equal dimensions will have equal height, length, and width, so it must be a cube.

With that in mind, we can find our side length by starting with the volume and working backward.

V=s^3

So, to find our side length, we just need to take the cubed root of the volume.

$s=\sqrt[3]{216m^3}=6m$

So, our answer is 6 meters, a fairly large crate!

Report an Error

Example Question #1 : How To Find The Length Of An Edge Of A Cube

If the volume of a cube is 30, what must be the length of the edge of the cube?

Possible Answers:

$\frac{10}{3}$

$\sqrt[3]{30}$

$\frac{\sqrt{10}}{3}$

$\sqrt{30}$

Correct answer:

$\sqrt[3]{30}$

Explanation:

Write the formula to find the volume of a cube.

V=s^3

Substitute the volume into the equation.

30=s^3

Cube root both sides.

$\sqrt[3]{30}=\sqrt[3]{s^3}$

The answer is: $\sqrt[3]{30}$

Report an Error

View Tutors

Gabby
Certified Tutor

University of Oregon, Bachelor in Arts, Journalism. University of Oregon, Current Grad Student, Communication, General.

View Tutors

Eva
Certified Tutor

Technicka Univerzita Liberec, Bachelor of Education, Education.

View Tutors

Jaleesa
Certified Tutor

Pomona College, Bachelors, Africana Studies.

All ISEE Upper Level Math Resources

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

Popular Subjects

Algebra Tutors in Dallas Fort Worth, Physics Tutors in Atlanta, Statistics Tutors in Washington DC, Algebra Tutors in New York City, ISEE Tutors in Philadelphia, LSAT Tutors in Dallas Fort Worth, MCAT Tutors in Seattle, Reading Tutors in Phoenix, Reading Tutors in Washington DC, Algebra Tutors in Boston

Popular Courses & Classes

Spanish Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Seattle, GMAT Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Seattle, GRE Courses & Classes in Phoenix, ACT Courses & Classes in Boston, GMAT Courses & Classes in Seattle, SSAT Courses & Classes in Houston, LSAT Courses & Classes in Phoenix

Popular Test Prep

LSAT Test Prep in Los Angeles, MCAT Test Prep in Denver, GMAT Test Prep in Seattle, ISEE Test Prep in Los Angeles, SAT Test Prep in Phoenix, GMAT Test Prep in Dallas Fort Worth, SSAT Test Prep in Los Angeles, SAT Test Prep in Miami, ISEE Test Prep in New York City, SSAT Test Prep in Seattle

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 : Solid Geometry

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #51 : Solid Geometry

Example Question #51 : Solid Geometry

Example Question #52 : Solid Geometry

Example Question #52 : Solid Geometry

Example Question #2 : Volume Of A Rectangular Solid

Example Question #52 : Solid Geometry

Example Question #1 : How To Find The Length Of An Edge Of A Cube

Example Question #371 : Geometry

Example Question #2 : How To Find The Length Of An Edge Of A Cube

Example Question #1 : How To Find The Length Of An Edge Of A Cube

All ISEE Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: