We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Solid Geometry

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Solid Geometry

What is the volume of a cone with a height of and a base with a radius of ?

Possible Answers:

$396\pi$

$507\pi$

$117\pi$

$1521\pi$

Correct answer:

$507\pi$

Explanation:

To find the volume of a cone we must use the equation $V=\frac{1}{3}(A_{base})(H)$ . In this formula, $A_{base}$ is the area of the circular base of the cone, and is the height of the cone.

We must first solve for the area of the base using r=13 .

The equation for the area of a circle is $A=\pi(r^{2})$ . Using this, we can adjust our formula and plug in the value of our radius.

$V=\frac{1}{3}(A_{base})(H)=\frac{1}{3}(\pi r^2)(H)=\frac{1}{3}(\pi (13)^2)(H)$

13^2=169

$V=\frac{1}{3}(169\pi)(H)$

Now we can plug in our given height, H=9 .

$V=\frac{1}{3}(169\pi)(9)$

Multiply everything out to solve for the volume.

$V=\frac{1}{3}(169\pi)(9)=(169\pi)(3)=507\pi$

The volume of the cone is $507\pi$ .

Report an Error

Example Question #2 : Solid Geometry

What is the equation of a circle with a center of (5,15) and a radius of 7?

Possible Answers:

(x-5)^2+(y-15)^2=49

(x+5)^2+(y+15)^2=49

(x-5)^2+(y-15)^2=14

(x-5)^2+(y-15)^2=7

Correct answer:

(x-5)^2+(y-15)^2=49

Explanation:

To find the equation of a circle we must first know the standard form of the equation of a circle which is

The letters and represent the -value and -value of the center of the circle respectively.

In this case is 5 and k is 15 so plugging the values into the equation yields (x-5)^2+(y-15)^2=r^2

We then plug the radius into the equation to get (x-5)^2+(y-15)^2=7^2

Square it to yield (x-5)^2+(y-15)^2=49

The equation with a center of (5,15) and a radius of 7 is (x-5)^2+(y-15)^2=49 .

Report an Error

Example Question #2 : Cones

$\textup{Find the volume, to the nearest cubic inch, of a cone with a radius of 8 inches}$

$\textup{at its base and a height of one foot.}$

Possible Answers:

2413

804

1206

302

Correct answer:

804

Explanation:

$V= \frac{1}{3} \pi r^{2}h\;\;\textup{Given: }r=8\textup{ inches}, h=12\textup{ inches}$

$V = \frac{1}{3} \pi\times8^{2}\times12\;\;\;\;\;V = 256\pi\;\;\;V=804.2$

Report an Error

Example Question #1 : Solid Geometry

What is the volume of a cone that has a radius of 3 and a height of 4?

Possible Answers:

$36\pi$

$4\pi$

$9\pi$

$12\pi$

Correct answer:

$12\pi$

Explanation:

The standard equation for the volume of a cone is

$v=\frac{1}{3}\pi (r)^2h$

where denotes the radius and denotes the height.

Plug in the given values for and to find the answer:

$v=\frac{1}{3}\pi (3)^2(4)=\frac{1}{3}\pi (9)(4)=12\pi$

Report an Error

Example Question #3 : Solid Geometry

Find the volume of the following cone.

Cone

Possible Answers:

$115 \pi m^3$

$130 \pi m^3$

$70 \pi m^3$

$100 \pi m^3$

$85 \pi m^3$

Correct answer:

$100 \pi m^3$

Explanation:

The formula for the volume of a cone is:

$V= \frac{\pi r^{2}h}{3}$

where is the radius of the cone and is the height of the cone.

In order to find the height of the cone, use the Pythagorean Theorem:

A^2 + B^2 = C^2

A^2 + (5m)^2 = (13m)^2

A^2 = 144m^2

A = 12m

Plugging in our values, we get:

$V= \frac{\pi (5m)^2 (12m)}{3}$

$V= \pi (25m^2)(4m)=100 \pi m^3$

Report an Error

Example Question #4 : Solid Geometry

Find the volume of the following cone.

Cone

Possible Answers:

$76 \pi m^3$

$96 \pi m^3$

$106 \pi m^3$

$116 \pi m^3$

$86 \pi m^3$

Correct answer:

$96 \pi m^3$

Explanation:

The formula for the volume of a cone is:

$V = \frac{\pi r^2 h}{3}$

Where is the radius of the cone and is the height of the cone

Use the Pythagorean Theorem to find the length of the radius:

A^2 + B^2 = C^2

A^2 + (8m)^2 = (10m)^2

A = 6m

Plugging in our values, we get:

$V = \frac{\pi (6m)^2 8m}{3}$

$V = 96 \pi m^3$

Report an Error

Example Question #1 : Cones

Find the volume of the following half cone.

Half_cone

Possible Answers:

$140 \pi m^3$

$170 \pi m^3$

$150 \pi m^3$

$160 \pi m^3$

$180 \pi m^3$

Correct answer:

$160 \pi m^3$

Explanation:

The formula of the volume of a half cone is:

$V=\frac{1}{3}(base)(height)$

$V = \frac{1}{3}\left(\frac{1}{2}\pi r^2\right)(h)$

Where is the radius of the cone and is the height of the cone.

Use the Pythagorean Theorem to find the height of the cone:

A^2+B^2 = C^2

A^2+(8m)^2=(17m)^2

A=15m

$V = \frac{1}{3}\left(\frac{1}{2}\pi (8m)^2\right)(15m)$

$V=160 \pi m^3$

Report an Error

Example Question #1 : Solid Geometry

What is the volume of a right cone with a diameter of 6 cm and a height of 5 cm?

Possible Answers:

$120\pi \ cm^{3}$

$15\pi \ cm^{3}$

$60\pi \ cm^{3}$

$180\pi \ cm^{3}$

$45\pi \ cm^{3}$

Correct answer:

$15\pi \ cm^{3}$

Explanation:

The general formula is given by $V = 1/3Bh = 1/3\pi r^{2}h$ , where = radius and = height.

The diameter is 6 cm, so the radius is 3 cm.

$V=\frac{\pi 3^2\times 5}{3}=15\pi$

Report an Error

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

There is a large cone with a radius of 4 meters and height of 18 meters. You can fill the cone with water at a rate of 3 cubic meters every 25 seconds. How long will it take you to fill the cone?

Possible Answers:

$600\ \textup{minutes}$

$800\ \textup{minutes}$

$60\ \textup{minutes}$

$3\ \textup{minutes}\ 20\ \textup{seconds}$

$41\ \textup{minutes}\ 53\ \textup{seconds}$

Correct answer:

$41\ \textup{minutes}\ 53\ \textup{seconds}$

Explanation:

First we will calculate the volume of the cone

$V=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi\cdot 4^{2}\cdot 18=96\pi\ m^{3}$

Next we will determine the time it will take to fill that volume

$96\pi \ m^{3}\times \frac{25\ s}{3\ m^{3}}=800\pi \ s$

We will then convert that into minutes

$800\pi \ s\times \frac{1\ minute}{60\ seconds}=13.\overline{3}\pi \ minutes\approx 41.9\ minutes\approx 41\ minutes\ 53\ seconds$

Report an Error

Example Question #3 : How To Find The Volume Of A Cone

You have an empty cylinder with a base diameter of 6 and a height of 10 and you have a cone full of water with a base radius of 3 and a height of 10. If you empty the cone of water into the cylinder, how much volume is left empty in the cylinder?

Possible Answers:

$45\pi$

$30\pi$

$60\pi$

$90\pi$

$120\pi$

Correct answer:

$60\pi$

Explanation:

Cylinder Volume = $\pi*r^{2}*h$

Cone Volume = $\frac{1}{3}*\pi*r^{2}*h$

Cylinder Diameter = 6, therefore Cylinder Radius = 3

Cone Radius = 3

Empty Volume = Cylinder Volume – Cone Volume

$=\pi*r^{2}*h-\frac{1}{3}*\pi*r^{2}*h$

$=\pi*3^{2}*10-\frac{1}{3}*\pi*3^{2}*10$

$=\pi*90-\pi*30$

$=\pi*60$

Report an Error

View Tutors

Anna
Certified Tutor

Nova Southeastern University, Master of Science, Education.

View Tutors

Dominica
Certified Tutor

Seton Hall University, Bachelor of Science, Business Administration and Management. Nova Southeastern University, Doctor of E...

View Tutors

Shimelis
Certified Tutor

Alemaya Uniersity of Agriculture, Bachelor, Agricultural Engineering. Alemaya University, Master's/Graduate, Agricultural Eng...

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Reading Tutors in Denver, Chemistry Tutors in Los Angeles, Algebra Tutors in Philadelphia, ISEE Tutors in Houston, ISEE Tutors in Seattle, Spanish Tutors in Washington DC, GMAT Tutors in San Diego, SAT Tutors in Washington DC, GMAT Tutors in Boston, Chemistry Tutors in Denver

Popular Courses & Classes

GMAT Courses & Classes in Philadelphia, MCAT Courses & Classes in Boston, Spanish Courses & Classes in Washington DC, GRE Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Washington DC, MCAT Courses & Classes in Denver, SAT Courses & Classes in Chicago, MCAT Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Atlanta, ACT Courses & Classes in Houston

Popular Test Prep

SAT Test Prep in San Diego, SSAT Test Prep in Denver, GMAT Test Prep in Philadelphia, ISEE Test Prep in Boston, LSAT Test Prep in Miami, LSAT Test Prep in Denver, SSAT Test Prep in Phoenix, GMAT Test Prep in Los Angeles, ACT Test Prep in Houston, ACT Test Prep in Chicago

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

High School Math : Solid Geometry

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Solid Geometry

Example Question #2 : Solid Geometry

Example Question #2 : Cones

Example Question #1 : Solid Geometry

Example Question #3 : Solid Geometry

Example Question #4 : Solid Geometry

Example Question #1 : Cones

Example Question #1 : Solid Geometry

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

Example Question #3 : How To Find The Volume Of A Cone

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: