We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

Create An Account

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Cubes

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:

5:1

15:1

125:1

100:1

25:1

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 #731 : Sat Mathematics

A cube is inscribed inside a sphere of radius 1 such that each of the eight vertices of the cube lie on the surface of the sphere. What is the volume of the cube?

Possible Answers:

$\frac{9\sqrt{3}}{8}$

$\frac{8\sqrt{3}}{9}$

$\frac{10\sqrt{3}}{7}$

$\frac{7\sqrt{3}}{10}$

Correct answer:

$\frac{8\sqrt{3}}{9}$

Explanation:

Cube

To make this problem easier to solve, we can inscribe a smaller square in the cube. In the diagram above, points A, B, C are midpoints of the edges of the inscribed cube. Therefore point , a vertex of the smaller cube, is also the center of the sphere. Point lies on the circumference of the sphere, so ED = 1 . is also the hypotenuse of right triangle FED . Similarly, is the hypotenuse of right triangle FBD . If we let BD = x , then, by the properties of a right triangle, $FD = x\sqrt2$ .

Using the Pythagorean Theorem, we can now solve for :

FD^2 + FE^2 = DE^2

$(x\sqrt{2})^2 + x^2 = 1^2$

2x^2 + x^2 = 1

3x^2 = 1

$x^2 = \frac{1}{3}$

$x=\sqrt{\frac{1}{3}}$

Since the side of the inscribed cube is , the volume is $V= (2x)^3=8x^3=8\sqrt{\frac{1}{3}}^3=\frac{8}{3\sqrt{3}}=\frac{8}{3\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}=\frac{8\sqrt{3}}{9}$ .

Report an Error

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

A perfect cube has a volume of 8 cubic centimeters. If the height, length and width of the cube were doubled, what would be the volume of the cube?

Possible Answers:

$64\:cm^3$

$24\:cm^3$

$48\:cm^3$

$16\:cm^3$

$128\:cm^3$

Correct answer:

$64\:cm^3$

Explanation:

Volume is calculated by height x width x length: $V=h\cdot w \cdot l$

For a cube, the height, width, and length are all the same value, so the equation can be simplified to V=s^3 , where is the length of one edge of the cube.

We know that for the initial cube, $V=8\:cm^3$ , so we can substitute this into the volume equation and solve for the length of one of the cube's sides:

V=s^3

8=s^3

$\sqrt[3]8=\sqrt[3]{s^3}$

2=s

So, one edge of the initial cube is $2\:cm$ long. When doubled, the cube will have edges that are each $4\:cm$ long. We can solve for the final volume of the cube by substituting $4\:cm$ into the equation for the volume of a cube and solving:

V=s^3

V=4^3

$V=4\cdot 4\cdot 4=64\:cm^3$

Report an Error

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

What's the volume of a cube with a length of 10a ?

Possible Answers:

300a^3

30a^3

100a^3

1000a^3

3600a^2

Correct answer:

1000a^3

Explanation:

Write the volume formula for a cube.

V=s^3

Substitute the side.

V=s^3=(10a)^3 = 1000a^3

Report an Error

Example Question #32 : Cubes

If the surface area of a cube is 30, what is the volume of the cube?

Possible Answers:

$5\sqrt5$

$\sqrt5$

$5\sqrt3$

125

900

Correct answer:

$5\sqrt5$

Explanation:

Write the surface area formula of the cube.

A=6s^2

Substitute the surface area and find the side.

30=6s^2

s^2=5

$s=\sqrt5$

Write the volume for the cube.

V=s^3

Substitute the side to the volume formula.

$V=s^3=5\sqrt5$

Report an Error

Example Question #735 : Geometry

The volumes of six cubes form an arithmetic sequence. The two smallest cubes have sidelengths 10 and 12, respectively. Give the volume of the largest cube.

Possible Answers:

4,640

1,920

5,368

8,000

2,400

Correct answer:

4,640

Explanation:

The volume of a cube is equal to the length of a side raised to the third power. The two smallest cubes will have volumes:

$V_{1} = 10^{3} = 1,000$

and

$V_{2} = 12^{3} = 1,728$ ,

respectively.

The volumes form an arithmetic sequence with these two volumes as the first two terms, so their common difference is

$d = V_{2} - V_{1} = 1,728 - 1,000 = 728$ .

The volume of the largest, or sixth-smallest, cube, is

$V_{6} = (6-1)d + V_{1}$

=5 (728) + 1,000

=3,640 + 1,000

= 4,640

Report an Error

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

Find the volume of a cube with side length 4.

Possible Answers:

254

Correct answer:

Explanation:

To solve, simply use the formula for the volume of a cube.

Substitute in the side length of four into the following equation.

Thus,

V=s^3=4^3=64

Report an Error

Example Question #14 : How To Find The Volume Of A Cube

Find the volume of a cube given side length is 1.

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for the volume of a cube. Thus,

V=s^3=1^3=1

Report an Error

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

A cube has a surface area of 150 . What is its volume?

Possible Answers:

150

125

100

Correct answer:

125

Explanation:

Remember that a cube's surface area, because it's comprised of six identical squares, can be stated as 6s^2 . With that in mind,

6s^2 = 150

s^2 = 25

$s = \sqrt{25} = 5$

The last step is easy: V = s^3 = 5^3 = 125

Report an Error

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

What is the volume of a cube with a side length of 7.5 cm?

(Round two the nearest two places)

Possible Answers:

274.63cm^2

421.88cm^3

512cm^2

857.38cm^3

Correct answer:

421.88cm^3

Explanation:

The formula for volume of a cube is,

V=s^3

where

s=side .

The side length of the cube is given as 7.5cm.

s=7.5

Substituting this into the formula for a cube's volume is as follows.

$\\V=(7.5)^3 \\V=(7.5)(7.5)(7.5) \\V=421.875\approx 421.88cm^3$

Report an Error

View SAT Mathematics Tutors

Paulkey
Certified Tutor

National Chiao Tung University, Bachelors, Computer Science & Information Engineering. University of Maryland Eastern Shore, ...

View SAT Mathematics Tutors

Sarah
Certified Tutor

New York University, Bachelor of Fine Arts, Drama.

View SAT Mathematics Tutors

Thomas
Certified Tutor

Michigan State University, Bachelor in Arts, History. Central Michigan University, Doctor of Philosophy, History.

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

SAT Math Tutors in Top Cities:

Atlanta SAT Math Tutors, Austin SAT Math Tutors, Boston SAT Math Tutors, Chicago SAT Math Tutors, Dallas Fort Worth SAT Math Tutors, Denver SAT Math Tutors, Houston SAT Math Tutors, Kansas City SAT Math Tutors, Los Angeles SAT Math Tutors, Miami SAT Math Tutors, New York City SAT Math Tutors, Philadelphia SAT Math Tutors, Phoenix SAT Math Tutors, San Diego SAT Math Tutors, San Francisco-Bay Area SAT Math Tutors, Seattle SAT Math Tutors, St. Louis SAT Math Tutors, Tucson SAT Math Tutors, Washington DC SAT Math Tutors

Popular Courses & Classes

SAT Courses & Classes in Boston, ISEE Courses & Classes in Phoenix, SAT Courses & Classes in Miami, LSAT Courses & Classes in Atlanta, ACT Courses & Classes in Phoenix, SSAT Courses & Classes in New York City, GMAT Courses & Classes in Seattle, Spanish Courses & Classes in Boston, SAT Courses & Classes in Denver, ISEE Courses & Classes in Denver

Popular Test Prep

GMAT Test Prep in New York City, ACT Test Prep in Phoenix, ISEE Test Prep in Dallas Fort Worth, LSAT Test Prep in Dallas Fort Worth, SAT Test Prep in Miami, SSAT Test Prep in New York City, LSAT Test Prep in Houston, GMAT Test Prep in Seattle, LSAT Test Prep in Atlanta, GRE Test Prep in Chicago

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

SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : Cubes

Example Question #731 : Sat Mathematics

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

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

Example Question #32 : Cubes

Example Question #735 : Geometry

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

Example Question #14 : How To Find The Volume Of A Cube

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

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

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: