We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : Intermediate Geometry

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 #52 : How To Find The Volume Of A Prism

Find the volume of the regular hexagonal prism.

Possible Answers:

4702.19

4509.17

4881.22

2314.89

Correct answer:

2314.89

Explanation:

Recall the formula to find the volume of any prism:

$\text{Volume of Prism}=\text{Area of base}\times \text{height}$

Since the base is a regular hexagon, recall how to find the area of a regular hexagon.

$\text{Area of Regular Hexagon}=\frac{3\sqrt3}{2}(\text{side})^2$

Plug in the given side to find the area of the base.

$\text{Area of Base}=\frac{3\sqrt3}{2}(9)^2=\frac{243\sqrt3}{2}$

Next, plug in the area of the base and the height to find the volume of the prism.

$\text{Volume of Prism}=\frac{243\sqrt3}{2} \times 11=2314.89$

Remember to round to places after the decimal.

Report an Error

Example Question #53 : How To Find The Volume Of A Prism

Find the volume of the regular hexagonal prism.

Possible Answers:

5972.98

25002.20

5992.11

25669.70

Correct answer:

5972.98

Explanation:

Recall the formula to find the volume of any prism:

$\text{Volume of Prism}=\text{Area of base}\times \text{height}$

Since the base is a regular hexagon, recall how to find the area of a regular hexagon.

$\text{Area of Regular Hexagon}=\frac{3\sqrt3}{2}(\text{side})^2$

Plug in the given side to find the area of the base.

$\text{Area of Base}=\frac{3\sqrt3}{2}(11)^2=\frac{363\sqrt3}{2}$

Next, plug in the area of the base and the height to find the volume of the prism.

$\text{Volume of Prism}=\frac{363\sqrt3}{2} \times 19=5972.98$

Remember to round to places after the decimal.

Report an Error

Example Question #54 : How To Find The Volume Of A Prism

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Find the volume of the figure.

Possible Answers:

190.24

157.70

151.24

167.23

Correct answer:

157.70

Explanation:

In order to find the volume of the figure, we will first need to find the volumes of the rectangular prism and the half cylinder.

From the figure, you should notice that the length of the prism is also the diameter of the half cylinder. Thus, half the length of the prism will also be the radius of the half cylinder. Also, notice that the width of the prism will be the height of the cylinder.

For the given cylinder then, find the radius.

$\text{radius}=\frac{\text{length}}{2}=\frac{4}{2}=2$

Then, recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi r^2 h$ , where is the radius and is the height.

Divide the volume by to find the volume of the half cylinder.

$\text{Volume of Half Cylinder}=\frac{\pi r^2 h}{2}$

$\text{Volume of Half Cylinder}=\frac{\pi (2^2)(6)}{2}=12\pi$

Next, recall how to find the volume of a rectangular prism.

$\text{Volume of Rectangular Prism}=\text{length}\times\text{width}\times\text{height}$

Plug in the given values to find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=(4)(6)(5)=120$

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

$\text{Volume of Figure}=\text{Volume of Half Cylinder}+\text{Volume of Rectangular Prism}$

$\text{Volume of Figure}=12\pi+120=157.70$

Remember to round to places after the decimal.

Report an Error

Example Question #55 : How To Find The Volume Of A Prism

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Find the volume of the figure.

Possible Answers:

390.24

405.78

401.10

424.96

Correct answer:

401.10

Explanation:

In order to find the volume of the figure, we will first need to find the volumes of the rectangular prism and the half cylinder.

For the given cylinder then, find the radius.

$\text{radius}=\frac{\text{length}}{2}=\frac{6}{2}=3$

Then, recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi r^2 h$ , where is the radius and is the height.

Divide the volume by to find the volume of the half cylinder.

$\text{Volume of Half Cylinder}=\frac{\pi r^2 h}{2}$

$\text{Volume of Half Cylinder}=\frac{\pi (3^2)(8)}{2}=36\pi$

Next, recall how to find the volume of a rectangular prism.

$\text{Volume of Rectangular Prism}=\text{length}\times\text{width}\times\text{height}$

Plug in the given values to find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=(6)(8)(6)=288$

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

$\text{Volume of Figure}=\text{Volume of Half Cylinder}+\text{Volume of Rectangular Prism}$

$\text{Volume of Figure}=36\pi+288=401.10$

Remember to round to places after the decimal.

Report an Error

Example Question #56 : How To Find The Volume Of A Prism

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Find the volume of the figure.

Possible Answers:

2221.20

2334.29

2501.20

2471.68

Correct answer:

2471.68

Explanation:

In order to find the volume of the figure, we will first need to find the volumes of the rectangular prism and the half cylinder.

For the given cylinder then, find the radius.

$\text{radius}=\frac{\text{length}}{2}=\frac{12}{2}=6$

Then, recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi r^2 h$ , where is the radius and is the height.

Divide the volume by to find the volume of the half cylinder.

$\text{Volume of Half Cylinder}=\frac{\pi r^2 h}{2}$

$\text{Volume of Half Cylinder}=\frac{\pi (6^2)(14)}{2}=252\pi$

Next, recall how to find the volume of a rectangular prism.

$\text{Volume of Rectangular Prism}=\text{length}\times\text{width}\times\text{height}$

Plug in the given values to find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=(12)(14)(10)=1680$

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

$\text{Volume of Figure}=\text{Volume of Half Cylinder}+\text{Volume of Rectangular Prism}$

$\text{Volume of Figure}=252\pi+1680=2471.68$

Remember to round to places after the decimal.

Report an Error

Example Question #81 : Prisms

A cylinder is cut in half and placed on top of a rectangular prism as shown by the figure below.

Find the volume of the figure.

Possible Answers:

867.11

897.26

901.20

822.45

Correct answer:

897.26

Explanation:

In order to find the volume of the figure, we will first need to find the volumes of the rectangular prism and the half cylinder.

For the given cylinder then, find the radius.

$\text{radius}=\frac{\text{length}}{2}=\frac{5}{2}$

Then, recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi r^2 h$ , where is the radius and is the height.

Divide the volume by to find the volume of the half cylinder.

$\text{Volume of Half Cylinder}=\frac{\pi r^2 h}{2}$

$\text{Volume of Half Cylinder}=\frac{\pi (\frac{5}{2})^2(15)}{2}=\frac{375}{8}\pi$

Next, recall how to find the volume of a rectangular prism.

$\text{Volume of Rectangular Prism}=\text{length}\times\text{width}\times\text{height}$

Plug in the given values to find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=(5)(15)(10)=750$

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

$\text{Volume of Figure}=\text{Volume of Half Cylinder}+\text{Volume of Rectangular Prism}$

$\text{Volume of Figure}=\frac{375}{8}\pi+750=897.26$

Remember to round to places after the decimal.

Report an Error

Example Question #82 : Prisms

A cylinder is cut in half and placed on top of a rectangular prism.

Find the volume of the figure.

Possible Answers:

264.08

252.21

253.01

266.78

Correct answer:

264.08

Explanation:

In order to find the volume of the figure, we will first need to find the volumes of the rectangular prism and the half cylinder.

For the given cylinder then, find the radius.

$\text{radius}=\frac{\text{length}}{2}=\frac{3}{2}$

Then, recall how to find the volume of a cylinder:

$\text{Volume of Cylinder}=\pi r^2 h$ , where is the radius and is the height.

Divide the volume by to find the volume of the half cylinder.

$\text{Volume of Half Cylinder}=\frac{\pi r^2 h}{2}$

$\text{Volume of Half Cylinder}=\frac{\pi (\frac{3}{2})^2(17)}{2}=\frac{153}{8}\pi$

Next, recall how to find the volume of a rectangular prism.

$\text{Volume of Rectangular Prism}=\text{length}\times\text{width}\times\text{height}$

Plug in the given values to find the volume of the rectangular prism.

$\text{Volume of Rectangular Prism}=(3)(17)(4)=204$

To find the volume of the figure, add the volume of the half cylinder and the volume of the rectangular prism together.

$\text{Volume of Figure}=\text{Volume of Half Cylinder}+\text{Volume of Rectangular Prism}$

$\text{Volume of Figure}=\frac{153}{8}\pi+204=264.08$

Remember to round to places after the decimal.

Report an Error

Example Question #83 : Prisms

A triangular prism with an equilateral triangle base is placed on top of a rectangular prism with a square base as shown by the figure below.

Find the volume of the figure.

Possible Answers:

1032.67

856.68

912.83

655.81

Correct answer:

912.83

Explanation:

In order to find the volume of the figure, we will first need to find the volume of the rectangular and triangular prisms.

Recall how to find the volume for any prism:

$\text{Volume of Prism}=\text{Area of base}\times \text{height}$

First find the volume of the rectangular prism:

$\text{Volume of Rectangular Prism}=(7)(7)(13)=637$

Next, find the volume of the triangular prism.

Notice that the length of the rectangular prism is the same as the side of the equilateral triangle that makes up one of the bases of the triangular prism.

Recall how to find the area of an equilateral triangle:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3}{4}(\text{side})^2$

Plug in the given side to find the area of the triangle.

$\text{Area of Equilateral Triangle}=\frac{\sqrt3}{4}(7^2)=\frac{49\sqrt3}{4}$

Next, notice that the width of the rectangular prism is also the height of the triangular prism.

Now, find the volume of the triangular prism.

$\text{Volume of Triangular Prism}=\frac{49\sqrt3}{4}(13)=\frac{637\sqrt3}{4}$

To find the volume of the entire figure, add the individual volumes together.

$\text{Volume of Figure}=\text{Volume of Rectangular Prism}+\text{Volume of Triangular Prism}$

$\text{Volume of Figure}=637+\frac{637\sqrt3}{4}=912.83$

Make sure to round to places after the decimal.

Report an Error

Example Question #83 : Prisms

A triangular prism with an equilateral triangle base is placed on top of a rectangular prism with a square base as shown by the figure below.

Find the volume of the figure.

Possible Answers:

6238.09

6363.69

6512.35

6448.56

Correct answer:

6448.56

Explanation:

In order to find the volume of the figure, we will first need to find the volume of the rectangular and triangular prisms.

Recall how to find the volume for any prism:

$\text{Volume of Prism}=\text{Area of base}\times \text{height}$

First find the volume of the rectangular prism:

$\text{Volume of Rectangular Prism}=(15)(15)(20)=4500$

Next, find the volume of the triangular prism.

Notice that the length of the rectangular prism is the same as the side of the equilateral triangle that makes up one of the bases of the triangular prism.

Recall how to find the area of an equilateral triangle:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3}{4}(\text{side})^2$

Plug in the given side to find the area of the triangle.

$\text{Area of Equilateral Triangle}=\frac{\sqrt3}{4}(15^2)=\frac{225\sqrt3}{4}$

Next, notice that the width of the rectangular prism is also the height of the triangular prism.

Now, find the volume of the triangular prism.

$\text{Volume of Triangular Prism}=\frac{225\sqrt3}{4}(20)=1125\sqrt3$

To find the volume of the entire figure, add the individual volumes together.

$\text{Volume of Figure}=\text{Volume of Rectangular Prism}+\text{Volume of Triangular Prism}$

$\text{Volume of Figure}=4500+1125\sqrt3=6448.56$

Make sure to round to places after the decimal.

Report an Error

Example Question #61 : How To Find The Volume Of A Prism

A triangular prism with an equilateral triangle base is placed on top of a rectangular prism with a square base as shown by the figure below.

Find the volume of the figure.

Possible Answers:

95.31

109.65

103.18

101.27

Correct answer:

103.18

Explanation:

In order to find the volume of the figure, we will first need to find the volume of the rectangular and triangular prisms.

Recall how to find the volume for any prism:

$\text{Volume of Prism}=\text{Area of base}\times \text{height}$

First find the volume of the rectangular prism:

$\text{Volume of Rectangular Prism}=(3)(3)(8)=72$

Next, find the volume of the triangular prism.

Notice that the length of the rectangular prism is the same as the side of the equilateral triangle that makes up one of the bases of the triangular prism.

Recall how to find the area of an equilateral triangle:

$\text{Area of Equilateral Triangle}=\frac{\sqrt3}{4}(\text{side})^2$

Plug in the given side to find the area of the triangle.

$\text{Area of Equilateral Triangle}=\frac{\sqrt3}{4}(3^2)=\frac{9\sqrt3}{4}$

Next, notice that the width of the rectangular prism is also the height of the triangular prism.

Now, find the volume of the triangular prism.

$\text{Volume of Triangular Prism}=\frac{9\sqrt3}{4}(8)=\frac{72\sqrt3}{4}=18\sqrt3$

To find the volume of the entire figure, add the individual volumes together.

$\text{Volume of Figure}=\text{Volume of Rectangular Prism}+\text{Volume of Triangular Prism}$

$\text{Volume of Figure}=72+18\sqrt3=103.18$

Make sure to round to places after the decimal.

Report an Error

View Tutors

Patricia
Certified Tutor

Southern Illinois University Edwardsville, Bachelor of Science, Elementary School Teaching. Southern Illinois University Edwa...

View Tutors

MrG
Certified Tutor

Long Island University-Brooklyn Campus, Master of Science, Applied Mathematics.

View Tutors

Magdy
Certified Tutor

Cairo University, Egypt, Bachelor of Science, Electrical Engineering. New Mexico State University-Main Campus, Doctor of Phil...

All Intermediate Geometry Resources

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

Popular Subjects

Math Tutors in San Francisco-Bay Area, GMAT Tutors in San Francisco-Bay Area, MCAT Tutors in Philadelphia, French Tutors in Philadelphia, Statistics Tutors in Phoenix, English Tutors in Boston, ACT Tutors in Chicago, MCAT Tutors in Dallas Fort Worth, Computer Science Tutors in New York City, GMAT Tutors in Miami

Popular Courses & Classes

MCAT Courses & Classes in Atlanta, SSAT Courses & Classes in Boston, ISEE Courses & Classes in Los Angeles, LSAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Los Angeles, SAT Courses & Classes in Washington DC, GMAT Courses & Classes in New York City, SSAT Courses & Classes in Atlanta, LSAT Courses & Classes in Denver, SAT Courses & Classes in Chicago

Popular Test Prep

GMAT Test Prep in New York City, GMAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Los Angeles, GRE Test Prep in New York City, GRE Test Prep in Dallas Fort Worth, MCAT Test Prep in Boston, LSAT Test Prep in Boston, GMAT Test Prep in Denver, MCAT Test Prep in Seattle, ISEE 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

Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #52 : How To Find The Volume Of A Prism

Example Question #53 : How To Find The Volume Of A Prism

Example Question #54 : How To Find The Volume Of A Prism

Example Question #55 : How To Find The Volume Of A Prism

Example Question #56 : How To Find The Volume Of A Prism

Example Question #81 : Prisms

Example Question #82 : Prisms

Example Question #83 : Prisms

Example Question #83 : Prisms

Example Question #61 : 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: