Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : How to find the volume of a cone

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 : Cones

An empty tank in the shape of a right solid circular cone has a radius of r feet and a height of h feet. The tank is filled with water at a rate of w cubic feet per second. Which of the following expressions, in terms of r, h, and w, represents the number of minutes until the tank is completely filled?

Possible Answers:

20w/(π(r²)(h))

π(r²)(h)/(60w)

π(r²)(h)/(20w)

180w/(π(r²)(h))

π(r²)(h)/(180w)

Correct answer:

π(r²)(h)/(180w)

Explanation:

The volume of a cone is given by the formula V = (πr²)/3. In order to determine how many seconds it will take for the tank to fill, we must divide the volume by the rate of flow of the water.

time in seconds = (πr²)/(3w)

In order to convert from seconds to minutes, we must divide the number of seconds by sixty. Dividing by sixty is the same is multiplying by 1/60.

(πr²)/(3w) * (1/60) = π(r²)(h)/(180w)

Report an Error

Example Question #202 : Psat Mathematics

A cone has a base radius of 13 in and a height of 6 in. What is its volume?

Possible Answers:

1352π in³

4394π in³

None of the other answers

338π in³

1014π in³

Correct answer:

338π in³

Explanation:

The basic form for the volume of a cone is:

V = (1/3)πr²h

For this simple problem, we merely need to plug in our values:

V = (1/3)π13²* 6 = 169 * 2π = 338π in³

Report an Error

Example Question #3 : Cones

A cone has a base circumference of 77π in and a height of 2 ft. What is its approximate volume?

Possible Answers:

11,858π in³

142,296π in³

71,148π in³

8893.5π in³

2964.5π in³

Correct answer:

11,858π in³

Explanation:

There are two things to be careful with here. First, we must solve for the radius of the base. Secondly, note that the height is given in feet, not inches. Notice that all the answers are in cubic inches. Therefore, it will be easiest to convert all of our units to inches.

First, solve for the radius, recalling that C = 2πr, or, for our values 77π = 2πr. Solving for r, we get r = 77/2 or r = 38.5.

The height, in inches, is 24.

The basic form for the volume of a cone is: V = (1 / 3)πr²h

For our values this would be:

V = (1/3)π * 38.5² * 24 = 8 * 1482.25π = 11,858π in³

Report an Error

Example Question #871 : Geometry

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

Possible Answers:

$15\pi \ cm^{3}$

$60\pi \ cm^{3}$

$45\pi \ cm^{3}$

$120\pi \ cm^{3}$

$180\pi \ cm^{3}$

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 : Solid Geometry

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:

$800\ \textup{minutes}$

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

$600\ \textup{minutes}$

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

$60\ \textup{minutes}$

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

Find the volume of a cone with a radius of and a height of .

Possible Answers:

$300\pi$

$9000\pi$

$900\pi$

$6000\pi$

$3000\pi$

Correct answer:

$3000\pi$

Explanation:

Write the formula to find the volume of a cone.

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

Substitute the known values and simplify.

$V=\frac{1}{3}\pi (10)^2 (90)= \frac{1}{3}\pi (100)(90)= \pi (100)(30)=3000\pi$

Report an Error

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

Find the volume of a cone with radius 3 and height 5.

Possible Answers:

$60\pi$

$45\pi$

$30\pi$

$15\pi$

Correct answer:

$15\pi$

Explanation:

To solve, simply use the formula for the volume of a cone. Thus,

$V=\frac{1}{3}\pi{r^2}h=\frac{1}{3}\pi*{3^2}*5=\frac{1}{3}\pi*9*5=15\pi$

To remember the formula for volume of a cone, it helps to break it up into it's base and height. The base is a circle and the height is just h. Now, just multiplying those two together would give you the formula of a cylinder (see problem 3 in this set). So, our formula is going to have to be just a portion of that. Similarly to volume of a pyramid, that fraction is one third.

Report an Error

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

Find the area of a cone whose radius is 4 and height is 3.

Possible Answers:

$64\pi$

$48\pi$

$16\pi$

$24\pi$

Correct answer:

$64\pi$

Explanation:

To solve, simply use the formula for the area of a cone. Thus,

$V=\frac{4}{3}\pi{r^2}h=\frac{4}{3}*\pi*4^2*3=4*\pi*16=64\pi$

Report an Error

Example Question #4 : How To Find The Volume Of A Cone

The volume of a right circular cone is $9\pi$ . If the cone's height is equal to its radius, what is the radius of the cone?

Possible Answers:

$\sqrt{27}$

$3\pi$

Correct answer:

Explanation:

The volume of a right circular cone with radius and height is given by:

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

Since the height of this cone is equal to its radius, we can say:

$V = \pi r^2 \frac{r}{3} = \frac{1}{3}\pi r^3$

Now, we can substitute our given volume into the equation and solve for our radius.

$9\pi = \frac{1}{3}\pi r^3$

$27\pi = \pi r^3$

27 = r^3

r = 3

Report an Error

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

Cone

The above is a right circular cone. Give its volume.

Possible Answers:

$175 \pi$

$49 \pi+35 \pi\sqrt{11}$

$294 \pi$

$\frac{245}{3} \pi \sqrt{11}$

$\frac{1,925}{3} \pi$

Correct answer:

$\frac{245}{3} \pi \sqrt{11}$

Explanation:

The volume of a right circular cone can be calculated from its height and the radius of its base using the formula

$V = \frac{1}{3} \pi r^{2} h$ .

We are given r = 7 , but not .

, , and the slant height of a right circular cone are related by the Pythagorean Theorem:

$h^{2}+ r^{2}= l^{2}$

Setting l = 18 and r = 7 , substitute and solve for :

$h^{2}+ 7^{2}= 18^{2}$

$h^{2}+49= 324$

$h^{2}+49 - 49 = 324 - 49$

$h^{2} =275$

Taking the square root of both sides and simplifying the radical:

$h =\sqrt{275} = \sqrt{25} \cdot \sqrt{11} = 5 \sqrt{11}$

Now, substitute for and and evaluate:

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

$V = \frac{1}{3} \pi \cdot 7^{2} \cdot 5 \sqrt{11}$

$V = \frac{1}{3} \pi \cdot 49 \cdot 5 \sqrt{11}$

$V = \frac{245}{3} \pi \sqrt{11}$

Report an Error

View SAT Mathematics Tutors

Cole
Certified Tutor

UW Madison, Bachelors, Industrial Engineering. UW Madison, Masters, Industrial Engineering.

View SAT Mathematics Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

View SAT Mathematics Tutors

Thomas
Certified Tutor

Michigan State University, Bachelor in Arts, History. Central Michigan University, Doctor of Philosophy, History.

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

LSAT Courses & Classes in Boston, Spanish Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Seattle, LSAT Courses & Classes in Los Angeles, LSAT Courses & Classes in Phoenix, SAT Courses & Classes in Philadelphia, ISEE Courses & Classes in San Diego, LSAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Phoenix, ISEE Courses & Classes in Los Angeles

Popular Test Prep

MCAT Test Prep in Miami, ISEE Test Prep in Miami, LSAT Test Prep in Atlanta, SAT Test Prep in Denver, MCAT Test Prep in Houston, LSAT Test Prep in San Diego, GRE Test Prep in San Diego, GRE Test Prep in Seattle, LSAT Test Prep in Boston, GRE Test Prep in Philadelphia

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 : How to find the volume of a cone

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : Cones

Example Question #202 : Psat Mathematics

Example Question #3 : Cones

Example Question #871 : Geometry

Example Question #1 : Solid Geometry

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

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

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

Example Question #4 : How To Find The Volume Of A Cone

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

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: