GMAT Math : Calculating the length of an edge of a tetrahedron

Study concepts, example questions & explanations for GMAT Math

Create An Account

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Calculating The Length Of An Edge Of A Tetrahedron

Suppose the volume of the tetrahedron is $\frac{1}{3}$ . What is the edge of the tetrahedron?

Possible Answers:

$\frac{\sqrt3}{3}$

$\frac{\sqrt2}{3}$

$\sqrt3$

$\sqrt2$

Correct answer:

$\sqrt2$

Explanation:

Write the formula to solve for the edge of a tetrahedron.

$e=\sqrt2 \sqrt[3]{3V}$

Substitute the volume and solve.

$e=\sqrt2 \sqrt[3]{3(\frac{1}{3})}= \sqrt2 \sqrt[3]{1}=\sqrt2$

Report an Error

Example Question #721 : Problem Solving Questions

The height of one of the equilateral triangle faces on a tetrahedron is $6\sqrt{3}$ . What is the side length of the tetrahedron?

Possible Answers:

$18\sqrt{5}$

$12\sqrt{3}$

$6\sqrt{6}$

Correct answer:

Explanation:

Because a tetrahedron has four congruent equilateral triangles as its faces, we know the three equal angles of each face, as with all equilateral triangles, are each $60^{\circ}$ . We are given the height of a face, which is the length of a line that bisects one of the $60^{\circ}$ angles and forms a right triangle with the side length as its hypotenuse. This means the angle between the height and the side length is $30^{\circ}$ , whose cosine is equal to the adjacent side, the height, over the hypotenuse, the side length. This gives us:

$\cos 30^{\circ}=\frac{h}{a}$

$\frac{\sqrt{3}}{2}=\frac{6\sqrt{3}}{a}$

$a=\frac{6\sqrt{3}}{\frac{\sqrt{3}}{2}}=6\sqrt{3}\cdot \frac{2}{\sqrt{3}}=12$

Report an Error

Example Question #1 : Calculating The Length Of An Edge Of A Tetrahedron

The volume of a tetrahedron is . What is the edge of the tetrahedron?

Possible Answers:

$9\sqrt3$

$3\sqrt3$

$3\sqrt2$

$9\sqrt2$

$\frac{3\sqrt3}{2}$

Correct answer:

$3\sqrt2$

Explanation:

Write the formula to solve for the edge of a tetrahedron.

$e=\sqrt2 \sqrt[3]{3V}$

Substitute the given volume to the equation and solve.

$e=\sqrt2 \sqrt[3]{3(9)}= \sqrt2 \sqrt[3]{27}=3\sqrt2$

Report an Error

Example Question #1 : Tetrahedrons

Find the exact edge length of a tetrahedron if the volume is .

Possible Answers:

$\sqrt[4]{18}$

$\sqrt2 \sqrt[3]{9}$

$3\sqrt2$

$\sqrt[3]{18}$

$\sqrt{11}$

Correct answer:

$\sqrt2 \sqrt[3]{9}$

Explanation:

Write the tetrahedron formula to solve for the edge.

$e=\sqrt2 \sqrt[3]{3V}$

Substitute the volume and simplify.

$e=\sqrt2 \sqrt[3]{3(3)}= \sqrt2 \sqrt[3]{9}$

Report an Error

Example Question #1 : Tetrahedrons

A certain tetrahedron has a surface area of $16\sqrt{3}$ . What is the length of an edge of the tetrahedron?

Possible Answers:

$\sqrt{3}$

$4\sqrt{3}$

Correct answer:

Explanation:

A tetrahedron has four congruent equilateral triangle faces, so its surface area is four times the area of one of these equilateral triangles. This gives us:

$SA=4\left(\frac{1}{2}bh\right)=2bh$

Where is the base of the triangle, or the edge length of the tetrahedron, and is the height of each triangular face. We want to solve for , but we are only given the surface area and not the height, so we need to express this value in terms of the base. One way of doing this is by recognizing that the height of each equilateral triangle face bisects an angle and forms two congruent right triangles for which it is the base and the edge length, or , is the hypotenuse. Each angle in an equilateral triangle is $60^{\circ}$ , so if one is bisected by the height then the angle between it and the hypotenuse is $30^{\circ}$ . The cosine of this angle is equal to the height over the hypotenuse, which gives us:

$\cos30^{\circ}=\frac{h}{b}\rightarrow h=b\cos30^{\circ}\rightarrow h=\frac{\sqrt{3}}{2}b$

Now that we have an expression for the height in terms of the base, we can plug this value into the equation for surface area and be left with only one unknown, the base that is equivalent to the edge length for which we want to solve:

$SA=2bh=2b\left(\frac{\sqrt{3}}{2}b\right)=\sqrt{3}b^2$

$16\sqrt{3}=\sqrt{3}b^2$

$b^2=16\rightarrow b=4$

Report an Error

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Physics Tutors in Seattle, Physics Tutors in San Francisco-Bay Area, Calculus Tutors in Seattle, Computer Science Tutors in Houston, Physics Tutors in Philadelphia, Reading Tutors in Dallas Fort Worth, GMAT Tutors in Washington DC, ACT Tutors in New York City, MCAT Tutors in Seattle, SSAT Tutors in Washington DC

Popular Courses & Classes

ACT Courses & Classes in New York City, MCAT Courses & Classes in Los Angeles, ACT Courses & Classes in Seattle, GMAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Washington DC, SAT Courses & Classes in Los Angeles, ACT Courses & Classes in Boston, ISEE Courses & Classes in New York City, MCAT Courses & Classes in San Diego, GRE Courses & Classes in Denver

Popular Test Prep

MCAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Dallas Fort Worth, GMAT Test Prep in Houston, GMAT Test Prep in Dallas Fort Worth, GMAT Test Prep in Phoenix, SAT Test Prep in Atlanta, ACT Test Prep in Chicago, ISEE Test Prep in Philadelphia, SAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Washington DC

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)

Email address:
Your name:
Feedback:

GMAT Math : Calculating the length of an edge of a tetrahedron

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Calculating The Length Of An Edge Of A Tetrahedron

Example Question #721 : Problem Solving Questions

Example Question #1 : Calculating The Length Of An Edge Of A Tetrahedron

Example Question #1 : Tetrahedrons

Example Question #1 : Tetrahedrons

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details