Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : How to find the volume of a prism

Study concepts, example questions & explanations for Intermediate Geometry

Create An Account

All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #94 : Prisms

Pyramid

The above figure shows a square pyramid inscribed inside a cube. The pyramid has volume 100. Give the volume of the cube.

Possible Answers:

200 $\displaystyle 200$

300 $\displaystyle 300$

$233\frac{1}{3}$ $\displaystyle 233\frac{1}{3}$

$333\frac{1}{3}$ $\displaystyle 333\frac{1}{3}$

250 $\displaystyle 250$

Correct answer:

300 $\displaystyle 300$

Explanation:

Let $\displaystyle s$ be the length of one side of the cube. Then the base of the pyramid is a square with sidelength $\displaystyle s$, and its area is

$B = s^{2}$ $\displaystyle B = s^{2}$.

The volume of a pyramid is one third the product of its height and the area of its base. The height of the pyramid is $\displaystyle s$, so the volume is

$V_{1} = \frac{1}{3} Bh = \frac{1}{3} s^{2} \cdot s = \frac{1}{3} s^{3}$ $\displaystyle V_{1} = \frac{1}{3} Bh = \frac{1}{3} s^{2} \cdot s = \frac{1}{3} s^{3}$

The volume of the cube is $V_{2} = s^{3}$ $\displaystyle V_{2} = s^{3}$, so

$V_{1} = \frac{1}{3} V_{2}$ $\displaystyle V_{1} = \frac{1}{3} V_{2}$

or, equivalently,

$3 \cdot V_{1} =3 \cdot \frac{1}{3} V_{2}$ $\displaystyle 3 \cdot V_{1} =3 \cdot \frac{1}{3} V_{2}$

$V_{2} = 3 \cdot V_{1}$ $\displaystyle V_{2} = 3 \cdot V_{1}$

That is, the volume of the cube is three times that of the pyramid, and, since the pyramid has volume 100, the volume of the cube is $3 \cdot 100 =300$ $\displaystyle 3 \cdot 100 =300$.

Report an Error

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

A rectangular box has two sides with the following lengths:

3$ cm$ $\displaystyle 3$ cm$$ and 4 $ cm$ $\displaystyle 4 $ cm$$

If it possesses a volume of $84$ cm$^{3}$ $\displaystyle 84$ cm$^{3}$, what is the area of its largest side?

Possible Answers:

Correct answer:

Explanation:

The volume of a rectangular prism is found using the following formula:

$V=l\times w\times h$ $\displaystyle V=l\times w\times h$

If we substitute our known values, then we can solve for the missing side.

$84=3\times 4\times x$ $\displaystyle 84=3\times 4\times x$

84=12x $\displaystyle 84=12x$

Divide both sides of the equation by 12.

$\frac{84}{12}=\frac{12x}{12}$ $\displaystyle \frac{84}{12}=\frac{12x}{12}$

x=7 $\displaystyle x=7$

We now know that the missing length equals 7 centimeters.

This means that the box can have sides with the following dimensions: 3cm by 4cm; 7cm by 3cm; or 7cm by 4cm. The greatest area of one side belongs to the one that is 7cm by 4cm.

$A=l\times w$ $\displaystyle A=l\times w$

$A=4\times 7$ $\displaystyle A=4\times 7$

A=28 $\displaystyle A=28$

Report an Error

View Tutors

Harshica
Certified Tutor

North Carolina State University at Raleigh, Bachelor of Science, Computer Science.

View Tutors

Cassandra
Certified Tutor

Eastern Michigan University, Bachelor of Education, Science Teacher Education.

View Tutors

Mikah
Certified Tutor

Ivy Tech Community College, Associate in Science, Biotechnology. Western Governors University, Bachelor in Business Administr...

All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in Miami, Physics Tutors in Atlanta, Spanish Tutors in Phoenix, Computer Science Tutors in Phoenix, ACT Tutors in San Francisco-Bay Area, Math Tutors in San Francisco-Bay Area, Algebra Tutors in Boston, SAT Tutors in Los Angeles, SAT Tutors in Denver, MCAT Tutors in Washington DC

Popular Courses & Classes

SAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Atlanta, SAT Courses & Classes in Philadelphia, ACT Courses & Classes in Atlanta, GRE Courses & Classes in Atlanta, GRE Courses & Classes in Boston, ACT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Miami, SSAT Courses & Classes in Miami, ISEE Courses & Classes in Chicago

Popular Test Prep

LSAT Test Prep in Denver, GRE Test Prep in Atlanta, GRE Test Prep in Los Angeles, ACT Test Prep in Atlanta, LSAT Test Prep in Dallas Fort Worth, SAT Test Prep in Dallas Fort Worth, SSAT Test Prep in Miami, SSAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Seattle, SAT Test Prep in Seattle

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

Intermediate Geometry : How to find the volume of a prism

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #94 : Prisms

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

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: