Call Now to Set Up Tutoring:

(888) 888-0446

Common Core: 8th Grade Math : Know and Use the Formulas for the Volumes of Cones, Cylinders, and Spheres: CCSS.Math.Content.8.G.C.9

Study concepts, example questions & explanations for Common Core: 8th Grade Math

Create An Account

All Common Core: 8th Grade Math Resources

7 Diagnostic Tests 75 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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

Chestnut wood has a density of about $0.45\frac{g}{cm^3}$ . A right circular cone made out of chestnut wood has a height of three meters, and a base with a radius of two meters. What is its mass in kilograms (nearest whole kilogram)?

Possible Answers:

$5,755 \; \textrm{kg}$

$5,955 \; \textrm{kg}$

$6,055 \; \textrm{kg}$

$5,855 \; \textrm{kg}$

$5,655 \; \textrm{kg}$

Correct answer:

$5,655 \; \textrm{kg}$

Explanation:

First, convert the dimensions to cubic centimeters by multiplying by 100 : the cone has height 300cm , and its base has radius 200cm .

$3m*\frac{100cm}{1m}=300cm\ \ \2m*\frac{100cm}{1m}=200cm$

Its volume is found by using the formula and the converted height and radius.

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

$V=\frac{1}{3} \pi (200cm)^{2} ( 300cm )\approx 12,566,371 \; \textrm{cm}^{3}$

Now multiply this by $0.45\frac{g}{cm^3}$ to get the mass.

$m=V*\rho$

$12,566,371cm^3*0.45\frac{g}{cm^3} \approx 5,654,867g$

Finally, convert the answer to kilograms.

$5654867g *\frac{1kg}{1,000g} \approx 5,655kg$

Report an Error

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

A cone has the height of 4 meters and the circular base area of 4 square meters. If we want to fill out the cone with water (density = $1000\frac{Kg}{m^3}$ ), what is the mass of required water (nearest whole kilogram)?

Possible Answers:

10,000

5333

6333

4333

2133

Correct answer:

5333

Explanation:

The volume of a cone is:

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

where is the radius of the circular base, and is the height (the perpendicular distance from the base to the vertex).

As the circular base area is $\pi r^2$ , so we can rewrite the volume formula as follows:

$Volume =\frac{A\times h}{3}$

where is the circular base area and known in this problem. So we can write:

$Volume =\frac{A\times h}{3}=\frac{4\times 4}{3}=\frac{16}{3}\approx 5.333 m^3$

We know that density is defined as mass per unit volume or:

$\rho =\frac{m}{v}$

Where $\rho$ is the density; is the mass and is the volume. So we get:

$m=\rho v=1000\times 5.333=5333 Kg$

Report an Error

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

The vertical height (or altitude) of a right cone is . The radius of the circular base of the cone is . Find the volume of the cone in terms of .

Possible Answers:

$\frac{1}{3}\pi t^3$

$\frac{2}{3}\pi t^3$

$\pi t^3$

$\frac{1}{3}\pi t^2$

$\frac{2}{3}\pi t^2$

Correct answer:

$\frac{2}{3}\pi t^3$

Explanation:

The volume of a cone is:

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

where is the radius of the circular base, and is the height (the perpendicular distance from the base to the vertex).

$Volume=\frac{1}3{}\pi r^2h =\frac{1}3{}\pi t^2\times 2t=\frac{2}{3}\pi t^3$

Report an Error

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

A right cone has a volume of $8\pi$ , a height of and a radius of the circular base of . Find .

Possible Answers:

$\sqrt{2}$

$2\sqrt[3]{2}$

$\sqrt[3]{3}$

$\sqrt[3]{2}$

Correct answer:

$\sqrt[3]{2}$

Explanation:

The volume of a cone is given by:

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

where is the radius of the circular base, and is the height; the perpendicular distance from the base to the vertex. Substitute the known values in the formula:

$Volume=\frac{1}{3}\pi r^2h\Rightarrow 8\pi=\frac{1}{3}\pi\times (2t)^2\times 3t$

$\Rightarrow 8\pi=4\pi t^3\Rightarrow t^3=2\Rightarrow t=\sqrt[3]{2}$

Report an Error

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

A cone has a diameter of $12\:m$ and a height of $4\:m$ . In cubic meters, what is the volume of this cone?

Possible Answers:

$54\pi\:m^3$

$36\pi\:m^3$

$48\pi\:m^3$

$144\pi\:m^3$

Correct answer:

$48\pi\:m^3$

Explanation:

First, divide the diameter in half to find the radius.

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

$\frac{12}{2}=6\:m$

Now, use the formula to find the volume of the cone.

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

$\text{Volume}=\frac{1}{3}\pi \times 6^2\times4=\frac{1}{3}\pi \times 36\times4=\frac{144}{3}\pi=48\pi\:m^3$

Report an Error

Example Question #111 : Volume Of A Three Dimensional Figure

The height of a cylinder is 3 inches and the radius of the circular end of the cylinder is 3 inches. Give the volume and surface area of the cylinder.

Possible Answers:

V=74.78 in^3, A=103.04in^2

V=84.78 in^3, A=123.04in^2

V=74.78 in^3, A=113.10in^2

V=84.78 in^3, A=103.04in^2

V=84.82 in^3, A=113.10in^2

Correct answer:

V=84.82 in^3, A=113.10in^2

Explanation:

The volume of a cylinder is found by multiplying the area of one end of the cylinder (base) by its height or:

$Volume=\pi r^2h$

where is the radius of the circular end of the cylinder and is the height of the cylinder. So we can write:

$Volume=\pi r^2h=\pi \times 3^2\times 3=84.82in^3$

The surface area of the cylinder is given by:

$A=2\pi r^2+2\pi rh$

where is the surface area of the cylinder, is the radius of the cylinder and is the height of the cylinder. So we can write:

$A=2\pi r^2+2\pi rh$

$A=2\pi (3)^2+2\pi \times 3\times 3$

$A=18\pi+18\pi$

$A=36\pi$

A=113.10

Report an Error

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

The height of a cylinder is two times the length of the radius of the circular end of a cylinder. If the volume of the cylinder is $16\pi$ , what is the height of the cylinder?

Possible Answers:

$2\sqrt{2}$

Correct answer:

Explanation:

The volume of a cylinder is:

$Volume=\pi r^2h$

where is the radius of the circular end of the cylinder and is the height of the cylinder.

Since h=2r , we can substitute that into the volume formula. So we can write:

$Volume=\pi r^2h$

$16\pi=\pi r^2\cdot (2r)$

$16\pi =2\pi r^{3}$

$16=2r^{3}$

$8=r^{3}$

r=2

So we get:

$h=2r=2\times 2=4$

Report an Error

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

The end (base) of a cylinder has an area of $16\pi$ square inches. If the height of the cylinder is half of the radius of the base of the cylinder, give the volume of the cylinder.

Possible Answers:

$8\pi$

$16\pi$

$32\pi$

Correct answer:

$32\pi$

Explanation:

The area of the end (base) of a cylinder is $\pi r^2$ , so we can write:

$\pi r^2=16\pi\Rightarrow r^2=16\Rightarrow r=4\ inches$

The height of the cylinder is half of the radius of the base of the cylinder, that means:

$h=\frac{r}{2}=\frac{4}{2}=2\ inches$

The volume of a cylinder is found by multiplying the area of one end of the cylinder (base) by its height:

$Volume=Area\times h=16\pi\times 2=32\pi$

$Volume=\pi r^2h=\pi\times 4^2\times 2=32\pi$

Report an Error

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

We have two right cylinders. The radius of the base Cylinder 1 is $\sqrt{3}$ times more than that of Cylinder 2, and the height of Cylinder 2 is 4 times more than the height of Cylinder 1. The volume of Cylinder 1 is what fraction of the volume of Cylinder 2?

Possible Answers:

$V_{1}=\frac{2}{3}V_{2}$

$V_{1}=V_{2}$

$V_{1}=\frac{3}{2}V_{2}$

$V_{1}=\frac{3}{4}V_{2}$

$V_{1}=\frac{4}{3}V_{2}$

Correct answer:

$V_{1}=\frac{3}{4}V_{2}$

Explanation:

The volume of a cylinder is:

$V=\pi r^2h$

where is the volume of the cylinder, is the radius of the circular end of the cylinder, and is the height of the cylinder.

So we can write:

$V_{1}=\pi (r_{1})^2h_{1}$

and

$V_{2}=\pi (r_{2})^2h_{2}$

Now we can summarize the given information:

$r_{1}=\sqrt{3}\cdot r_{2}$

$h_{2}=4\cdot h_{1}\Rightarrow h_{1}=\frac{h_{2}}{4}$

Now substitute them in the $V_{1}$ formula:

$V_{1}=\pi (\sqrt{3}r_{2})^2\times \frac{h_{2}}{4}\Rightarrow V_{1}=\frac{3}{4}\pi (r_{2})^2\times h_{2}\Rightarrow V_{1}=\frac{3}{4}V_{2}$

Report an Error

Example Question #1 : Know And Use The Formulas For The Volumes Of Cones, Cylinders, And Spheres: Ccss.Math.Content.8.G.C.9

Two right cylinders have the same height. The radius of the base of the first cylinder is two times more than that of the second cylinder. Compare the volume of the two cylinders.

Possible Answers:

$V_{1}=3\cdot V_{2}$

$V_{1}=V_{2}$

$V_{1}=2\cdot V_{2}$

$V_{1}=\sqrt{2}\cdot V_{2}$

$V_{1}=4\cdot V_{2}$

Correct answer:

$V_{1}=4\cdot V_{2}$

Explanation:

The volume of a cylinder is:

$V=\pi r^2h$

where is the radius of the circular end of the cylinder and is the height of the cylinder. So we can write:

$V_{1}=\pi (r_{1})^2h_{1}$

$V_{2}=\pi (r_{2})^2h_{2}$

We know that

$h_{1}=h_{2}$

and

$r_{1}=2r_{2}$ .

So we can write:

$V_{1}=\pi (r_{1})^2h_{1}=\pi (2r_{2})^2\cdot h_{2}=4\pi (r_{2})^2h_{2}\Rightarrow V_{1}=4V_{2}$

Report an Error

View Tutors

Ingy
Certified Tutor

University of Minnesota-Twin Cities, Bachelors, Mathematics with Actuarial Science Specialization.

View Tutors

Sarah
Certified Tutor

New York University, Bachelor of Fine Arts, Drama.

View Tutors

Justin
Certified Tutor

University of Toledo, Bachelors, Environmental Science. University of Michigan, Masters, Natural Resource Management.

All Common Core: 8th Grade Math Resources

7 Diagnostic Tests 75 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Reading Tutors in Denver, ISEE Tutors in San Diego, Physics Tutors in San Diego, Biology Tutors in Los Angeles, Calculus Tutors in San Diego, MCAT Tutors in Chicago, French Tutors in San Diego, Biology Tutors in San Diego, LSAT Tutors in Houston, Math Tutors in San Diego

Popular Courses & Classes

MCAT Courses & Classes in San Diego, ACT Courses & Classes in Chicago, SAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in San Diego, ISEE Courses & Classes in Houston, LSAT Courses & Classes in Chicago, GRE Courses & Classes in Houston, ACT Courses & Classes in Miami, GMAT Courses & Classes in New York City, Spanish Courses & Classes in San Francisco-Bay Area

Popular Test Prep

SSAT Test Prep in Denver, GMAT Test Prep in Seattle, ISEE Test Prep in Houston, SAT Test Prep in Seattle, SSAT Test Prep in Seattle, GRE Test Prep in Los Angeles, MCAT Test Prep in Houston, SSAT Test Prep in Washington DC, SAT Test Prep in Denver, 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

Common Core: 8th Grade Math : Know and Use the Formulas for the Volumes of Cones, Cylinders, and Spheres: CCSS.Math.Content.8.G.C.9

Study concepts, example questions & explanations for Common Core: 8th Grade Math

All Common Core: 8th Grade Math Resources

Example Questions

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

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

Example Question #2 : 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 #111 : Volume Of A Three Dimensional Figure

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

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 : Know And Use The Formulas For The Volumes Of Cones, Cylinders, And Spheres: Ccss.Math.Content.8.G.C.9

All Common Core: 8th Grade Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: