We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(202) 779-1569

ISEE Upper Level Math : Pyramids

Study concepts, example questions & explanations for ISEE Upper Level Math

Create An Account

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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

A pyramid has height 4 feet. Its base is a square with sidelength 3 feet. Give its volume in cubic inches.

Possible Answers:

$20,736 \textrm{ in}^{3}$

$62,208 \textrm{ in}^{3}$

$5,184\textrm{ in}^{3}$

$31,104\textrm{ in}^{3}$

$124,416\textrm{ in}^{3}$

Correct answer:

$20,736 \textrm{ in}^{3}$

Explanation:

Convert each measurement from inches to feet by multiplying it by 12:

Height: 4 feet = $4 \times 12 = 48$ inches

Sidelength of the base: 3 feet = $3 \times 12 = 36$ inches

The volume of a pyramid is

$V = \frac{1}{3} Bh$

Since the base is a square, we can replace $B = s^{2}$ :

$V = \frac{1}{3} s ^{2}h$

Substitute s=36, h = 48

$V = \frac{1}{3} \cdot 36 ^{2}\cdot 48$

V =20,736

The pyramid has volume 20,736 cubic inches.

Report an Error

Example Question #2 : How To Find The Volume Of A Pyramid

A 300 foot tall pyramid has a square base measuring feet on each side. What is the volume of the pyramid?

Possible Answers:

$160,000 ft^{2}$

$480,000 ft^{3}$

$4,000 ft^{3}$

$160,000 ft^{3}$

$12,000 ft^{3}$

Correct answer:

$160,000 ft^{3}$

Explanation:

In order to find the area of a triangle, we use the formula $\frac{1}{3}Bh$ . In this case, since the base is a square, we can replace with $s^{2}$ , so our formula for volume is $\frac{1}{3}s^{2}h$ .

Since the length of each side of the base is feet, we can substitute it in for .

$\frac{1}{3}\cdot (40)^{2}\cdot h$

We also know that the height is 300 feet, so we can substitute that in for .

$\frac{1}{3}\cdot (40)^{2}\cdot 300$

This gives us an answer of $160,000 ft^{3}$ .

It is important to remember that volume is expressed in units cubed.

Report an Error

Example Question #2 : How To Find The Volume Of A Pyramid

The height of a right pyramid is feet. Its base is a square with sidelength feet. Give its volume in cubic inches.

Possible Answers:

$15,552 \textrm{ in}^{3}$

$62,208\textrm{ in}^{3}$

$41,472 \textrm{ in}^{3}$

$10,368 \textrm{ in}^{3}$

$31,104 \textrm{ in}^{3}$

Correct answer:

$10,368 \textrm{ in}^{3}$

Explanation:

Convert each of the measurements from feet to inches by multiplying by .

Height: $2 \times 12 = 24$ inches

Sidelength of base: $3 \times 12 = 36$ inches

The base of the pyramid has area

$B = s^{2} = 36^{2} = 1,296$ square inches.

Substitute B = 1,296, h = 24 into the volume formula:

$V = \frac {1}{3} Bh$

$V = \frac {1}{3} \cdot 1,296 \cdot 24 =10,368$ cubic inches

Report an Error

Example Question #2 : Solid Geometry

The height of a right pyramid is inches. Its base is a square with sidelength inches. Give its volume in cubic feet.

Possible Answers:

$4 \frac {2}{3} \textrm{ ft}^3$

$2 \frac {1}{3} \textrm{ ft}^3$

$4 \textrm{ ft}^3$

$9 \frac {1}{3} \textrm{ ft}^3$

$14 \textrm{ ft}^3$

Correct answer:

$4 \frac {2}{3} \textrm{ ft}^3$

Explanation:

Convert each of the measurements from inches to feet by dividing by .

Height: $42 \div 12 = 3 \frac{1}{2}$ feet

Sidelength: $24 \div 12 = 2$ feet

The base of the pyramid has area

$B = s^{2} = 2^{2} = 4$ square feet.

Substitute $B = 4, h = 3 \frac{1}{2}$ into the volume formula:

$V = \frac {1}{3} Bh$

$V = \frac {1}{3}\cdot 4 \cdot 3 \frac{1}{2}$

$V = \frac {1}{3} \cdot \frac {4}{1} \cdot \frac{7}{2}$

$V = \frac {1}{3} \cdot \frac {2}{1} \cdot \frac{7}{1} = \frac {14}{3} = 4 \frac {2}{3}$ cubic feet

Report an Error

Example Question #2 : Solid Geometry

The height of a right pyramid and the sidelength of its square base are equal. The perimeter of the base is 3 feet. Give its volume in cubic inches.

Possible Answers:

$81 \textrm{ in}^{3}$

$243 \textrm{ in}^{3}$

$576 \textrm{ in}^{3}$

$27 \textrm{ in}^{3}$

$729 \textrm{ in}^{3}$

Correct answer:

$243 \textrm{ in}^{3}$

Explanation:

The perimeter of the square base, feet, is equivalent to $3 \times 12 = 36$ inches; divide by to get the sidelength of the base - and the height: $36 \div 4 = 9$ inches.

The area of the base is therefore $B = s^{2} = 9^{2} = 81$ square inches.

In the formula for the volume of a pyramid, substitute B = 81,h=9 :

$V = \frac{1}{3} Bh = \frac{1}{3}\cdot 81 \cdot 9 = 243$ cubic inches.

Report an Error

Example Question #2 : Pyramids

What is the volume of a pyramid with the following measurements?

$length=7; width=6;height=9;slant\ length=11$

Possible Answers:

126

378

462

154

Correct answer:

126

Explanation:

The volume of a pyramid can be determined using the following equation:

$V=\frac{1}{3}lwh=\frac{1}{3}(7)(6)(9)=126$

Report an Error

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

A right regular pyramid with volume 1,000 has its vertices at the points

(0,0,0), (n,0, 0), (n,n,0), (0, n, n), (n,n,n)

where n > 0 .

Evaluate .

Possible Answers:

n = 10

n = 30

$n = 10 \sqrt[3]{3 }$

$n = 10 \sqrt[3]{2}$

n = 20

Correct answer:

$n = 10 \sqrt[3]{3 }$

Explanation:

The pyramid has a square base that is units by units, and its height is units, as can be seen from this diagram,

Pyramid

The square base has area $B = n^{2}$ ; the pyramid has volume $V = \frac{1}{3} \cdot n^{2} \cdot n = \frac{1}{3} n^{3}$

Since the volume is 1,000, we can set this equal to 1,000 and solve for :

$\frac{1}{3} n^{3} = 1,000$

$n^{3} = 3,000$

$n = \sqrt[3]{3,000} = \sqrt[3]{1,000} \cdot \sqrt[3]{3 } = 10 \sqrt[3]{3 }$

Report an Error

Example Question #323 : Geometry

Find the volume of a pyramid with the following measurements:

length = 4in
width = 3in
height = 5in

Possible Answers:

$20\text{in}^3$

$80\text{in}^3$

$60\text{in}^3$

$12\text{in}^3$

$40\text{in}^3$

Correct answer:

$20\text{in}^3$

Explanation:

To find the volume of a pyramid, we will use the following formula:

$V = \frac{l \cdot w \cdot h}{3}$

where l is the length, w is the width, and h is the height of the pyramid.

Now, we know the base of the pyramid has a length of 4in. We also know the base of the pyramid has a width of 3in. We also know the pyramid has a height of 5in.

Knowing this, we can substitute into the formula. We get

$V = \frac{4\text{in} \cdot 3\text{in} \cdot 5\text{in}}{3}$

$V = \frac{60\text{in}^3}{3}$

$V = 20\text{in}^3$

Report an Error

Example Question #324 : Geometry

Find the volume of a pyramid with the following measurements:

length = 4cm
width = 9cm
height = 8cm

Possible Answers:

$24\text{cm}^3$

$126\text{cm}^3$

$288\text{cm}^3$

$96\text{cm}^3$

$154\text{cm}^3$

Correct answer:

$96\text{cm}^3$

Explanation:

To find the volume of a pyramid, we will use the following formula:

$V = \frac{l \cdot w \cdot h}{3}$

where l is the length, w is the width, and h is the height of the pyramid.

Now, we know the following measurements:

length = 4cm
width = 9cm
height = 8cm

Knowing this, we can substitute into the formula. We get

$V = \frac{4\text{cm} \cdot 9\text{cm} \cdot 8\text{cm}}{3}$

$V = \frac{288\text{cm}^3}{3}$

$V = 96\text{cm}^3$

Report an Error

Example Question #325 : Geometry

Find the volume of a pyramid with the following measurements:

length: 7in
width: 6in
height: 8in

Possible Answers:

$336\text{in}^3$

$426\text{in}^3$

$168\text{in}^3$

$112\text{in}^3$

$221\text{in}^3$

Correct answer:

$112\text{in}^3$

Explanation:

To find the volume of a pyramid, we will use the following formula:

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

where l is the length, w is the width, and h is the height of the pyramid.

Now, we know the following measurements:

length: 7in
width: 6in
height: 8in

So, we get

$V = \frac{ 7\text{in} \cdot 6\text{in} \cdot 8\text{in}}{3}$

$V = \frac{42\text{in}^2 \cdot 8\text{in}}{3}$

$V = \frac{336\text{in}^3}{3}$

$V = 112\text{in}^3$

Report an Error

View Tutors

Beverly
Certified Tutor

Wesleyan University, Bachelors, Mathematics. The University of Texas at Arlington, Masters, Linguistics.

View Tutors

Muhammad
Certified Tutor

Iowa State University, Bachelor of Science, Management Information Systems. Lahore University of Management Sciences, Masters...

View Tutors

Straley
Certified Tutor

Johns Hopkins University, Bachelor of Science, Public Health. Johns Hopkins University, Master of Science, International Heal...

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Algebra Tutors in Washington DC, Calculus Tutors in Los Angeles, LSAT Tutors in San Diego, Physics Tutors in Phoenix, GRE Tutors in Boston, Algebra Tutors in Miami, MCAT Tutors in Miami, Chemistry Tutors in Seattle, Calculus Tutors in Seattle, Computer Science Tutors in Los Angeles

Popular Courses & Classes

Spanish Courses & Classes in Denver, GRE Courses & Classes in Seattle, LSAT Courses & Classes in Chicago, GMAT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Atlanta, MCAT Courses & Classes in San Diego, ACT Courses & Classes in Houston, MCAT Courses & Classes in Seattle, GMAT Courses & Classes in New York City, SAT Courses & Classes in Phoenix

Popular Test Prep

MCAT Test Prep in Los Angeles, LSAT Test Prep in Seattle, GMAT Test Prep in Denver, GMAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Phoenix, LSAT Test Prep in New York City, LSAT Test Prep in Washington DC, ISEE Test Prep in Miami, MCAT Test Prep in Chicago, MCAT Test Prep in San Francisco-Bay Area

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

ISEE Upper Level Math : Pyramids

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

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

Example Question #2 : How To Find The Volume Of A Pyramid

Example Question #2 : How To Find The Volume Of A Pyramid

Example Question #2 : Solid Geometry

Example Question #2 : Solid Geometry

Example Question #2 : Pyramids

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

Example Question #323 : Geometry

Example Question #324 : Geometry

Example Question #325 : Geometry

All ISEE Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: