We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : Pyramids

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

If the height of a pyramid was increased by 20% and a side of the square base was decreased 30%, what would happen to the volume of the pyramid?

Possible Answers:

There is a 59% increase in volume

It would have the same volume

59% decrease in volume

There is a 41% decrease in volume

There is no way to know if it would increase or decrease in volume

Correct answer:

There is a 41% decrease in volume

Explanation:

First, you will want to create a pyramid with measurements that are easy to calculate. So, let's say that we have pyramid with a base edge of 10 inches and a height of 10 inches.

So the volume of the original pyramid would be equal to

$\frac{(10\times 10)(10)}{3}=\frac{1000}{3}=333.33\: inches^2$

The volume of the altered pyramid would be equal to:

$\frac{(7\times 7)(12)}{3}=\frac{588}{3}=196\: inches^2$

To find the relationship between the volume of the altered pyramid relative to the volume of the original pyramid, divide the altered volume by the original volume.

$\frac{196}{333.33}=.59$

The new volume is 59% of the original volume, which means there was a 41% decrease in volume.

Report an Error

Example Question #1 : Pyramids

The Pyramid of Giza has a height of 480 feet. If the length of each side of the base is approximately 756 feet, what is its total surface area? Round to the nearest tenth.

Possible Answers:

$934,416 ft^{2}$

$802,494 ft^{2}$

$1,495,368 ft^{2}$

$752,976 ft^{2}$

Correct answer:

$1,495,368 ft^{2}$

Explanation:

If the length of one side is 756 ft, then multiply to find the area of the base.

$\text{Area of square} = \text{length} \times \text{width}$

$A=756\times756$

$A=571,536 ft^{2}$

Once you've found the area of the base, use the height of the pyramid and half of the side length of the base to determine the length of the side from the apex to the ground using the Pythagorean Theorem.

$480^{2}+378^{2}=c^{2}$

$230,400+142,884=c^{2}$

$373,284=c^{2}$

611=c

Using the side length of the base and the height of each of the triangles that form the pyramid, calculate the area of each triangle, then multiply by 4.

$\text{Area of a triangle}=\frac{1}{2}\times \text{base} \times \text{height}$

$A=\frac{1}{2} \times 611 \times 756$

A=230,958

$\text{Area of four triangles} = 4 \times 230,958$

$A=923,832 ft^{2}$

Add the surface area of the base to the surface area of the four triangles.

$\text{Total surface area} = 571,536 + 923,832$

$1,495,368 ft^{2}$

Report an Error

Example Question #2 : 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

432

$\frac{17}{3}$

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 : Pyramids

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:

$12\ cm^3$

$25\ cm^3$

$24\ cm^3$

$10\ cm^3$

$30\ cm^3$

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 #3 : Pyramids

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

32in.^3

60in.^3

48in.^3

36in.^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

Nicholas
Certified Tutor

Fordham University, Bachelors, Business Administration and Management. Boston University, Masters, Media Ventures.

View SAT Mathematics Tutors

Scott
Certified Tutor

Rutgers College, Bachelors, Political Science and Government. Florida Coastal School of Law, PHD, Law.

View SAT Mathematics Tutors

Noah
Certified Tutor

Bard College, Bachelors, Philosophy and Creative Writing (Dual Major). Sarah Lawrence College, Master of Fine Arts, Creative ...

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

MCAT Courses & Classes in San Diego, Spanish Courses & Classes in Atlanta, SSAT Courses & Classes in Los Angeles, LSAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Phoenix, ACT Courses & Classes in Washington DC, GRE Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Seattle, GRE Courses & Classes in Boston, GMAT Courses & Classes in Miami

Popular Test Prep

ACT Test Prep in Washington DC, ACT Test Prep in San Francisco-Bay Area, GRE Test Prep in Dallas Fort Worth, ACT Test Prep in Phoenix, LSAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Denver, GRE Test Prep in Chicago, LSAT Test Prep in Chicago, SAT Test Prep in Atlanta, GMAT Test Prep in Phoenix

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 : Pyramids

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : Pyramids

Example Question #1 : Pyramids

Example Question #2 : Pyramids

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

Example Question #52 : Solid Geometry

Example Question #4 : Pyramids

Example Question #3 : Pyramids

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: