Call Now to Set Up Tutoring:

(888) 888-0446

PSAT Math : How to find the volume of a cone

Study concepts, example questions & explanations for PSAT Math

Create An Account

All PSAT Math Resources

10 Diagnostic Tests 421 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:

π(r²)(h)/(180w)

180w/(π(r²)(h))

π(r²)(h)/(60w)

π(r²)(h)/(20w)

20w/(π(r²)(h))

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 #1 : How To Find The Volume Of A Cone

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

Possible Answers:

None of the other answers

1352π in³

338π in³

1014π in³

4394π 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:

8893.5π in³

142,296π in³

11,858π in³

71,148π 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 #1 : How To Find The Volume Of A Cone

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

Possible Answers:

$120\pi \ cm^{3}$

$180\pi \ cm^{3}$

$60\pi \ cm^{3}$

$45\pi \ cm^{3}$

$15\pi \ cm^{3}$

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 : Cones

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:

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

$60\ \textup{minutes}$

$600\ \textup{minutes}$

$800\ \textup{minutes}$

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

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 #2 : Cones

Cone

Which of these answers comes closest to the volume of the above cone?

Possible Answers:

$0.48\textup{ m}^{3}$

$0.34\textup{ m}^{3}$

$0.29 \textup{ m}^{3}$

$0.44\textup{ m}^{3}$

$0.32\textup{ m}^{3}$

Correct answer:

$0.29 \textup{ m}^{3}$

Explanation:

The radius and the height of a cone are required in order to find its volume.

The radius is 50 centimeters, which can be converted to meters by dividing by 100:

$50 \div 100 = 0.5$ meters

The slant height is 120 centimeters, which converts similarly to

$120 \div 100 = 1.2$ meters

To find the height, we need to use the Pythagorean Theorem with the radius 0.5 as one leg and the slant height 1.2 as the hypotenuse of a right triangle, and the height as the other leg:

$h = \sqrt{1.2^{2} -0.5^{2}} = \sqrt{1.44 -0.25} = \sqrt{1.19} \approx 1.09$ meters.

The volume formula can now be used:

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

$\approx \frac{3.14 \cdot 0.5^{2} \cdot 1.09}{3}$

$\approx \frac{3.14 \cdot 0.25 \cdot 1.09}{3}$

$\approx \frac{0.8557}{3}$

$\approx 0.29$ cubic meters

Report an Error

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

What is the volume of a cone with a height of $12\textup{\textup{ inches}}$ and base radius of $5\textup{ inches}$ ?

Possible Answers:

$100\pi\textup{ cubic inches}$

$20\pi\textup{ cubic inches}$

$300\pi\textup{ cubic inches}$

$150\pi\textup{ cubic inches}$

$60\pi\textup{ cubic inches}$

Correct answer:

$100\pi\textup{ cubic inches}$

Explanation:

The fomula for the volume of a cone is

v=(1/3)(b)(h) $\textup{where }b\textup{ is the area of the base, and }h\textup{ is the height}$

Because our radius of the base is $5\textup{ inches}$ , we know that $area=\pi r^2=25\pi$ .

$v=\left ( \frac{1}{3} \right )(12)(25\pi)=100\pi$ .

Report an Error

View PSAT Mathematics Tutors

Yongmao
Certified Tutor

Nankai University, Bachelor of Science, Chemistry. Washington University in St Louis, Doctor of Philosophy, Organic Chemistry.

View PSAT Mathematics Tutors

Rene Solo
Certified Tutor

University of the Philippines, Bachelor of Science, Mathematics. Prairie View A & M University, Master of Arts, Educational A...

View PSAT Mathematics Tutors

Shakeel
Certified Tutor

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ACT Tutors in Miami, SSAT Tutors in Houston, Algebra Tutors in Seattle, LSAT Tutors in San Francisco-Bay Area, Computer Science Tutors in Miami, SAT Tutors in Los Angeles, MCAT Tutors in Washington DC, Math Tutors in Chicago, MCAT Tutors in San Francisco-Bay Area, Chemistry Tutors in Los Angeles

Popular Courses & Classes

ISEE Courses & Classes in New York City, GRE Courses & Classes in Los Angeles, GMAT Courses & Classes in Los Angeles, SAT Courses & Classes in Los Angeles, SAT Courses & Classes in Washington DC, LSAT Courses & Classes in Chicago, MCAT Courses & Classes in San Diego, MCAT Courses & Classes in Houston, Spanish Courses & Classes in New York City, SSAT Courses & Classes in Washington DC

Popular Test Prep

GRE Test Prep in Philadelphia, LSAT Test Prep in Houston, MCAT Test Prep in Atlanta, GRE Test Prep in San Francisco-Bay Area, GMAT Test Prep in Boston, ISEE Test Prep in New York City, SAT Test Prep in Seattle, SAT Test Prep in Miami, LSAT Test Prep in San Diego, MCAT 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

PSAT Math : How to find the volume of a cone

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : Cones

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

Example Question #3 : Cones

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

Example Question #1 : Cones

Example Question #2 : Cones

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

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: