We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : How to find the volume of a pyramid

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 : Pyramids

The volume of a 6-foot-tall square pyramid is 8 cubic feet. How long are the sides of the base?

Possible Answers:

$2\ ft$

$4\ ft$

$4\ ft^{2}$

$1.5\ ft$

$2\ ft^{2}$

Correct answer:

$2\ ft$

Explanation:

Volume of a pyramid is

$\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (height)$

Thus:

$8=\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (6)$

$8=2\cdot (Area\ of\ the\ base)$

Area of the base is $4\ ft^{2}$ .

Therefore, each side is $2\ ft$ .

Report an Error

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

A right pyramid with a square base has a height that is twice the length of one edge of the base. If the height of the pyramid is 6 meters, find the volume of the pyramid.

Possible Answers:

Correct answer:

Explanation:

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters.

Since the base is a square, the area of the base is 3 x 3 = 9.

Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

Report an Error

Example Question #52 : Solid Geometry

Find the volume of the pyramid shown below:

Screen shot 2015 10 27 at 3.33.57 pm

Possible Answers:

689

$\frac{17}{3}$

432

144

Correct answer:

144

Explanation:

The formula for the area of a pyramid is $\frac{lwh}{3}$ . In this case, the length is , the width is , and the height is .

$8\times6\times9=432$ and $439\div3=144$ .

Report an Error

Example Question #4 : How To Find The Volume Of A Pyramid

Pyramid question

Figure not drawn to scale

In the pyramid above, the base is a square. The distance between points C and D is 6 inches and the length of side b is 5 inches. What is the volume of this pyramid?

Possible Answers:

$12\ cm^3$

$10\ cm^3$

$25\ cm^3$

$30\ cm^3$

$24\ cm^3$

Correct answer:

$24\ cm^3$

Explanation:

Pyramid question notes1

To find the volume of a pyramid, you need to use the equation below:

$Volume=\frac{(area\, of\, the\, base)(height)}{3}$

To find the height (shown by the yellow line), we can draw a right triangle using the yellow line, blue line and side b (5 inches). Because the hypotenuse is 5 inches, using the common Pythagorean 3-4-5 triple. The blue line is 3 inches and the yellow line (height) is 4 inches. Also, to find side a, we can use the blue line (3 inches) and half of the red line (3 inches) and the Pythagorean Theorum.

$3^2+3^2=(side\, a)^2$

$9+9=(side\, a)^2$

$18=(side\, a)^2$

$\sqrt{18}\, in=side\, a$

Because the base is a square, the area of the base is equal to the square of side a:

$(side a)^2=18\: in^2$

Now we plug in these values to find the volume:

$Volume=\frac{(18)(4)}{3}$

$Volume=\frac{(72)}{3}$

$Volume=24\, in^3$

Report an Error

Example Question #53 : Solid Geometry

Pyramid

Calculate the volume of the rectangular pyramid with height h=4in. , base width w=6in. , and base length l=6in.

Possible Answers:

72in.^3

48in.^3

36in.^3

32in.^3

60in.^3

Correct answer:

48in.^3

Explanation:

The volume of a rectangular pyramid with height , base width , and base length is given by

$V=\frac{1}{3}lwh$ .

For this pyramid, h=4in. , w=6in. , and l=6in. To calculate its volume, substitute the values for , , and into the formula:

$V=\frac{1}{3}(6)(6)(4)=\frac{144}{3}=48$

Therefore, the volume of the given rectangular pyramid is 48in.^3

Report an Error

View SAT Mathematics Tutors

Alexandra
Certified Tutor

Emerson College, Bachelor of Fine Arts, Creative Writing. Georgia State University, Doctor of Philosophy, Astronomy.

View SAT Mathematics Tutors

Amanda
Certified Tutor

Seattle University, Current Undergrad Student, Applied Mathematics.

View SAT Mathematics Tutors

Chase
Certified Tutor

Western Governors University, Bachelor of Science, Mathematics.

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

ACT Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Boston, GMAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Miami, LSAT Courses & Classes in Houston, ISEE Courses & Classes in Washington DC, LSAT Courses & Classes in Denver, GRE Courses & Classes in Boston, ISEE Courses & Classes in New York City, GRE Courses & Classes in Phoenix

Popular Test Prep

GMAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Phoenix, LSAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in New York City, SAT Test Prep in San Diego, ACT Test Prep in Dallas Fort Worth, SAT Test Prep in Chicago, ISEE Test Prep in New York City, GRE Test Prep in Phoenix, LSAT Test Prep in Dallas Fort Worth

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 volume of a pyramid

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : Pyramids

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

Example Question #52 : Solid Geometry

Example Question #4 : How To Find The Volume Of A Pyramid

Example Question #53 : Solid Geometry

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: