Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : Solid Geometry

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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

The height of a right circular cylinder is and its radius is . What is the volume, in cubic meters, of the cylinder?

Possible Answers:

$45\pi$

$30\pi$

$75\pi$

$15\pi$

$9\pi$

Correct answer:

$45\pi$

Explanation:

The volume of a right circular cylinder is equal to its height () multiplied by the area of the circle base ( $\pi r^2$ ).

In this scenario, the Volume

$V=5* (\pi *3^2) = 45\pi$ .

Therefore, the volume is $45\pi$ .

Report an Error

Example Question #121 : Solid Geometry

What is the volume of a cylinder with a radius of four inches and a height of seven inches?

Possible Answers:

112 inches^2

$784 \pi inches^3$

$196 \pi inches^3$

$112\pi inches^3$

$3256 \pi inches^3$

Correct answer:

$112\pi inches^3$

Explanation:

Plug the radius and height into the formula for the volume of a cylinder:
$\\V = \pi *r^2*h \newline V = \pi * 4^2 * 7 \newline V = 112 \pi inches^3$

Report an Error

Example Question #7 : Cylinders

What is the volume of a cylinder with a base diameter of 12 and a height of 3? Leave your answer in terms of $\pi$

Possible Answers:

$36\pi$

$100\pi$

$54\pi$

108

$108\pi$

Correct answer:

$108\pi$

Explanation:

To find the volume of a cylinder use formula:

$V = \pi r^2*h$

For a cylinder with a radius of 6 and a height of 3 this yields:

$V = \pi 6^2*3$

$=108\pi$

Report an Error

Example Question #2 : How To Find The Volume Of A Cylinder

Find the volume of a cylinder whose diameter is and height is .

Possible Answers:

$288\pi$

$24\pi$

$72\pi$

$48\pi$

Correct answer:

$72\pi$

Explanation:

To find volume, simply use the following formula. Remember, you were given diameter so radius is half of that. Thus,

$V=\pi{r^2}h=\pi*3^2*8=72\pi$

Report an Error

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

Find the volume of cylinder with diameter of and height of .

Possible Answers:

$36\pi$

$18\pi$

$24\pi$

$12\pi$

$72\pi$

Correct answer:

$18\pi$

Explanation:

To find volume of a cylinder, simply use the following formula. Thus,

$\textup{volume}=\pi{r^2}h=\pi*(3^2)*2=\pi*9*2=18\pi$

Report an Error

Example Question #1 : Cylinders

Find the volume fo a cylinder whose radius is and height is .

Possible Answers:

$11\pi$

$44\pi$

$22\pi$

Correct answer:

$11\pi$

Explanation:

To solve, simply use the formula. Thus,

$V=\pi{r^2}h=\pi\cdot1^2\cdot11=\pi\cdot1\cdot11=11\pi$

Report an Error

Example Question #11 : How To Find The Volume Of A Cylinder

Find the volume of a cylinder with height 1 and radius 1.

Possible Answers:

$3\pi$

$4\pi$

$2\pi$

$\pi$

Correct answer:

$\pi$

Explanation:

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

First, identify what is known.

Height = 1

Radius = 1

Substitute these values into the formula and solve.

Thus,

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

Report an Error

Example Question #12 : How To Find The Volume Of A Cylinder

Find the volume of a cylinder given height of and radius of .

Possible Answers:

$64\pi$

$32\pi$

$128\pi$

$16\pi$

Correct answer:

$32\pi$

Explanation:

To solve, simply use the following formula. Thus,

$V=\pi{r^2}h=\pi*2^2*8=\pi*4*8=32\pi$

Report an Error

Example Question #13 : Cylinders

A cylindrical tank is used as part of a water purifying plant. When contaminated water flows into the top section of the tank, pressure forces it through a mesh filter at the bottom of the tank and clean water exits through a funnel, leaving sediment behind. The tank's filter must be replaced when the total sediment content of the tank exceeds ten percent of the tank's total volume. If the tank is 100 feet tall and 18 feet in diameter, how much sediment, in cubic feet, can the drum hold before the filter must be changed?

Possible Answers:

$900\pi$

$760\pi$

$810\pi$

$8100\pi$

$9000\pi$

Correct answer:

$810\pi$

Explanation:

The volume of a cylinder is found using the following formula:

$V = \pi r^2 h$

In this formula, the variable is the height of the cylinder and is its radius. Since the diameter is two times the radius, first solve for the radius.

$\text{Diameter}=2r$

18=2r

Divide both sides of the equation by 2.

$\frac{18}{2}=\frac{2r}{}2$

r=9

The given cylinder has a radius of 9 feet. Now, substitute the calculated and known values into the equation for the volume of a cylinder and solve.

$V=\pi\times9^{2}\times 100$

$V=8100\pi$

This is the total volume of the tank. The question asks for the volume of ten percent of the tank—the point at which the filter must be replaced. To find this, move the decimal point in the numerical measure of total volume to the left one place in order to calculate ten percent of the total volume. (Ignore $\pi$ —you can treat it like a multiplier here. Since it appears on both sides of the equals sign, it doesn't affect the decimal shift.)

$8100\pi\times 0.10=810\pi$

The tank can hold $810\pi$ cubic feet of sediment before the filter needs to be changed.

Report an Error

Example Question #11 : Cylinders

What is the surface area of a cylinder with a radius of 2 cm and a height of 10 cm?

Possible Answers:

40π cm²

36π cm²

56π cm²

48π cm²

32π cm²

Correct answer:

48π cm²

Explanation:

SA_cylinder = 2πrh + 2πr² = 2π(2)(10) + 2π(2)² = 40π + 8π = 48π cm²

Report an Error

View ACT Math Tutors

Jhemson
Certified Tutor

Batangas State University, Doctor of Philosophy, Mathematics.

View ACT Math Tutors

Christopher
Certified Tutor

University of Michigan-Ann Arbor, Bachelor of Science, Computer Science.

View ACT Math Tutors

Nimil
Certified Tutor

University of Calgary, Master's/Graduate, Mechanical and Manufacturing Engineering.

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors

Popular Courses & Classes

ACT Courses & Classes in Seattle, GRE Courses & Classes in Phoenix, LSAT Courses & Classes in Miami, Spanish Courses & Classes in Phoenix, LSAT Courses & Classes in Washington DC, ISEE Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Denver, Spanish Courses & Classes in Seattle, SSAT Courses & Classes in Atlanta, GRE Courses & Classes in Denver

Popular Test Prep

GRE Test Prep in San Diego, GRE Test Prep in Phoenix, MCAT Test Prep in Washington DC, SSAT Test Prep in Philadelphia, GRE Test Prep in Los Angeles, MCAT Test Prep in Denver, SAT Test Prep in Chicago, SSAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in San Diego, LSAT Test Prep in Washington DC

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

ACT Math : Solid Geometry

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

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

Example Question #121 : Solid Geometry

Example Question #7 : Cylinders

Example Question #2 : How To Find The Volume Of A Cylinder

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

Example Question #1 : Cylinders

Example Question #11 : How To Find The Volume Of A Cylinder

Example Question #12 : How To Find The Volume Of A Cylinder

Example Question #13 : Cylinders

Example Question #11 : Cylinders

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: