We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : How to find the length of an edge of a prism

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 : How To Find The Length Of An Edge Of A Prism

For a box to fit inside the cupboard, the sum of the height and the perimeter of the box must, at most, be 360 cm. If Jenn has a box that has a height of 40 cm and a length of 23 cm, what is the greatest possible width of the box?

Possible Answers:

0.4 cm

297 cm

13 cm

137 cm

207 cm

Correct answer:

137 cm

Explanation:

First we write out the equation we are given. H + (2L +2W) = 360. H = 40 and L = 23

40 + (2(23) + 2W) = 360

40 + (46 + 2W) = 360

46 + 2W = 320

2W = 274

W = 137

Report an Error

Example Question #751 : Geometry

The volume of a rectangular prism is 80 cm³. The length, width, and height of the prism are each an integer number of cm. If the dimensions form three terms of an arithmetic sequence, find the average of the three dimensions.

Possible Answers:

Correct answer:

Explanation:

Method 1:

Trial and error to find a combination of factors of 80 that differ by the same amount will eventually yield 2, 5, 8. The average is 5.

Method 2:

Three terms of an arithmetic sequence can be written as x, x+d, and x+2d. Multiply these together using the distributive property to find the volume and the following equation results:

x³ + 3dx² + 2d²x - 80 = 0

Find an integer value of x that creates an integer solution for d. Try x=1 and we see the equation 1 + 3d + 2d² - 80 = 0 or 2d² + 3d -79 = 0. The determinant of this quadratic is 641, which is not a perfect square. Therefore, d is not an integer when x=1.

Try x=2 and we see the equation 8 + 12d + 4d² - 80 = 0 or d² + 3d - 18 = 0. This is easily factored to (d+6)(d-3)=0 so d=-6 or d=3. Since a negative value of d will result in negative dimensions of the prism, d must equal 3. Therefore, when substituting x=2 and d=3, the dimensions x, x+d, and x+2d become 2, 5, and 8. The average is 5.

Report an Error

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

A right rectangular prism has a volume of 64 cubic units. Its dimensions are such that the second dimension is twice the length of the first, and the third is one-fourth the dimension of the second. What are its exact dimensions?

Possible Answers:

1 x 4 x 16

4 x 4 x 4

2 x 4 x 8

1 x 2 x 32

3 x 6 x 12

Correct answer:

2 x 4 x 8

Explanation:

Based on our prompt, we can say that the prism has dimensions that can be represented as:

Dim1: x

Dim2: 2 * Dim1 = 2x

Dim3: (1/4) * Dim2 = (1/4) * 2x = (1/2) * x

More directly stated, therefore, our dimensions are: x, 2x, and 0.5x. Therefore, the volume is x * 2x * 0.5x = 64, which simplifies to x³ = 64. Solving for x, we find x = 4. Therefore, our dimensions are:

x = 4

2x = 8

0.5x = 2

Or: 2 x 4 x 8

Report an Error

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

A right rectangular prism has a volume of 120 cubic units. Its dimensions are such that the second dimension is three times the length of the first, and the third dimension is five times the dimension of the first. What are its exact dimensions?

Possible Answers:

4 x 12 x 20

None of the other answers

2 x 6 x 10

2 x 5 x 12

1 x 5 x 24

Correct answer:

2 x 6 x 10

Explanation:

Based on our prompt, we can say that the prism has dimensions that can be represented as:

Dim1: x

Dim2: 3 * Dim1 = 3x

Dim3: 5 * Dim1 = 5x

More directly stated, therefore, our dimensions are: x, 3x, and 5x. Therefore, the volume is x * 3x * 5x = 120, which simplifies to 15x³ = 120 or x³ = 8. Solving for x, we find x = 2. Therefore, our dimensions are:

x = 2

3x = 6

5x = 10

Or: 2 x 6 x 10

Report an Error

Example Question #751 : Sat Mathematics

The length of a crate is three-fourths its height and two-thirds its width. The surface area of the crate is 12 square meters. To the nearest centimeter, give the length of the box.

Possible Answers:

The correct answer is not among the other responses.

$111 \textrm{ cm}$

$144\textrm{ cm}$

$313 \textrm{ cm}$

$160 \textrm{ cm}$

Correct answer:

$111 \textrm{ cm}$

Explanation:

Call , , and the length, height, and width of the crate.

The length of the crate is two-thirds its width, so

$L = \frac{2}{3} W$

$\frac{3} {2} \cdot L = \frac{3} {2} \cdot \frac{2}{3} W$

$\frac{3} {2} L = W$

The length of the crate is three-fourths its height, so

$L = \frac{3}{4} H$

$\frac{4} {3} \cdot L = \frac{4} {3} \cdot \frac{3}{4} H$

$\frac{4} {3} L = H$

The dimensions of the crate in terms of are , $\frac{3} {2} L$ , and $\frac{4} {3} L$ . The surface area is found using the formula:

A = 2 (LW + LH + WH)

Substitute:

2 (LW + LH + WH) =A

$2\left ( L \cdot \frac{3} {2} L + L \cdot \frac{4} {3} L + \frac{3} {2} L \cdot \frac{4} {3} L \right ) =12$

$2\left ( \frac{3} {2} L^{2} + \frac{4} {3} L^{2} +2 L^{2} \right ) =12$

$2\left ( \frac{29} {6} L^{2} \right ) =12$

$\frac{29} {3} L^{2} =12$

Solve for :

$\frac{3} {29} \cdot \frac{29} {3} L^{2} =\frac{3} {29} \cdot 12$

$L^{2} =\frac{36} {29}$

$L =\sqrt{\frac{36} {29}}$

$L \approx 1.114$ meters.

Since one meter comprises 100 centimeters, multiply by 100 to convert to centimeters:

$1.114 \times 100 = 111.4$

This rounds to 111 centimeters.

Report an Error

Example Question #1 : Prisms

Box 3

The shaded face of the above rectangular prism is a square. If the volume of the prism is , give in terms of .

Possible Answers:

$x = \frac{V}{625}$

$x = \frac{\sqrt{V}}{625}$

$x = \frac{\sqrt{V}}{25}$

$x = \frac{\sqrt{V}}{5}$

$x = \frac{V}{25}$

Correct answer:

$x = \frac{V}{625}$

Explanation:

Since the top face of the prism is a square, the common sidelength - and the missing dimension - is 25.

The volume of a rectangular prism is equal to the product of its length, width, and height - that is,

LWH =V

Setting H= x, L=W= 25 , and solving for :

$25 \cdot 25 \cdot x =V$

625 x =V

$\frac{625 x }{625} =\frac{V}{625}$

$x = \frac{V}{625}$

Report an Error

View SAT Mathematics Tutors

Priyanka
Certified Tutor

CUNY Hunter College, Bachelor in Arts, Economics.

View SAT Mathematics Tutors

Joy
Certified Tutor

Boston University, Bachelor in Arts, Conservation Biology.

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

LSAT Courses & Classes in Miami, SAT Courses & Classes in Houston, MCAT Courses & Classes in Philadelphia, SSAT Courses & Classes in Atlanta, SAT Courses & Classes in Denver, SSAT Courses & Classes in San Diego, SAT Courses & Classes in New York City, ACT Courses & Classes in Houston, LSAT Courses & Classes in Houston, SAT Courses & Classes in Los Angeles

Popular Test Prep

ACT Test Prep in Boston, GRE Test Prep in Phoenix, LSAT Test Prep in San Diego, SSAT Test Prep in Seattle, GRE Test Prep in Houston, SAT Test Prep in Miami, MCAT Test Prep in Atlanta, SAT Test Prep in San Diego, LSAT Test Prep in Los Angeles, SAT Test Prep in Los Angeles

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 : How to find the length of an edge of a prism

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

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

Example Question #751 : Geometry

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

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

Example Question #751 : Sat Mathematics

Example Question #1 : Prisms

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: