We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SSAT Upper Level Math : Volume of a Three-Dimensional Figure

Study concepts, example questions & explanations for SSAT Upper Level Math

Create An Account

All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #3 : Volume Of A Sphere

A car dealership wants to fill a large spherical advertising ballon with helium. It can afford to buy 1,000 cubic yards of helium to fill this balloon. What is the greatest possible diameter of that balloon (nearest tenth of a yard)?

Possible Answers:

$6.2 \;\textrm{yd}$

$15.4 \;\textrm{yd}$

$7.7 \;\textrm{yd}$

$9.3 \;\textrm{yd}$

$12.4 \;\textrm{yd}$

Correct answer:

$12.4 \;\textrm{yd}$

Explanation:

The volume of a sphere, given its radius, is

$V = \frac{4\pi r^{3}}{3}$

Set V = 1,000 , solve for , and double that to get the diameter.

$1,000= \frac{4\pi r^{3}}{3}$

$r^{3} = \frac{1,000 \cdot 3 }{4\pi} \approx 238.7$

$r \approx \sqrt[3]{238.7} \approx 6.2$

The diameter is twice this, or 12.4 yards.

Report an Error

Example Question #11 : Know And Use The Formulas For The Volumes Of Cones, Cylinders, And Spheres: Ccss.Math.Content.8.G.C.9

The diameter of a sphere is . Give the volume of the sphere in terms of .

Possible Answers:

$72\pi t^3$

$30\pi t^3$

$10\pi t^3$

$36\pi t^3$

$24\pi t^3$

Correct answer:

$36\pi t^3$

Explanation:

The diameter of a sphere is so the radius of the sphere would be $6t\div 2=3t$

The volume enclosed by a sphere is given by the formula:

$Volume=\frac{4}{3}\pi r^3=\frac{4}{3}\pi \times (3t)^3=\frac{4}{3}\pi\times 27t^3\Rightarrow Volume=36\pi t^3$

Report an Error

Example Question #12 : Know And Use The Formulas For The Volumes Of Cones, Cylinders, And Spheres: Ccss.Math.Content.8.G.C.9

A spherical balloon has a diameter of 10 meters. Give the volume of the balloon.

Possible Answers:

523.6m^3

1000m^3

723.3m^3

1023.3m^3

500m^3

Correct answer:

523.6m^3

Explanation:

The volume enclosed by a sphere is given by the formula:

$Volume=\frac{4}{3}\pi r^3$

where is the radius of the sphere. The diameter of the balloon is 10 meters so the radius of the sphere would be $10\div 2=5$ meters. Now we can get:

$Volume=\frac{4}{3}\pi r^3=\frac{4}{3}\pi\times 5^3=\frac{4}{3}\times \pi \times 125\approx 523.6 m^3$

Report an Error

Example Question #3 : Volume Of A Three Dimensional Figure

The volume of a sphere is 1000 cubic inches. What is the diameter of the sphere.

Possible Answers:

$12\ inches$

$10\ inches$

$16.4\ inches$

$12.4\ inches$

$10.4\ inches$

Correct answer:

$12.4\ inches$

Explanation:

The volume of a sphere is:

$Volume=\frac{4}{3}\pi r^3$

Where is the radius of the sphere. We know the volume and can solve the formula for :

$Volume=\frac{4}{3}\pi r^3=1000\Rightarrow r^3=\frac{3\times1000 }{4\pi}\approx 238.85\Rightarrow r\approx 6.2$ inches

So we can get:

$Diameter=2r=2\times 6.2=12.4inches$

Report an Error

Example Question #621 : Geometry

A sphere has a diameter of inches. What is the volume of this sphere?

Possible Answers:

523.6 in^3

458.3 in^3

104.7 in^3

632.9 in^3

Correct answer:

523.6 in^3

Explanation:

To find the volume of a sphere, use the following formula:

$\text{Volume}=\frac{4}{3}\pi\times r^3$ , where is the radius of the sphere.

Now, because we are given the diameter of the sphere, divide that value in half to find the radius.

$r=10\div2=5$

Now, plug this value into the volume equation.

$\text{Volume}=\frac{4}{3}\pi\times 5^3$

$\text{Volume}=\frac{4}{3}\pi\times 125$

$\text{Volume}=\frac{500}{3}\pi=523.6$ in^3

Report an Error

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

What is the volume of a sphere with a diameter of ?

Possible Answers:

$\frac{500}{3}\pi$

$150\pi$

$100\pi$

$200\pi$

$\frac{100}{3}\pi$

Correct answer:

$\frac{500}{3}\pi$

Explanation:

Write the formula for the volume of the sphere.

$V=\frac{4}{3}\pi r^3$

The radius is half the diameter, which is five. Substitute the value.

$V=\frac{4}{3}\pi r^3=\frac{4}{3}\pi (5)^3=\frac{4}{3}\pi (125)= \frac{500}{3}\pi$

Report an Error

Example Question #1 : Volume Of A Three Dimensional Figure

What is the volume of a sphere with diameter 12 feet?

Possible Answers:

$7,238.2\;ft^{3}$

$904.8 ft^{3}$

$3,619.1\;ft^{2}$

$452.4\;ft^{3}$

None of the other answers are correct

Correct answer:

$904.8 ft^{3}$

Explanation:

The radius of the sphere is half the diameter, or 6 feet; use the formula

$V= \frac{4}{3} \pi r^{3}$ .

Setting r=6 :

$V= \frac{4}{3} \pi \cdot 6^{3} \approx904.8 ft^{3}$

Report an Error

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:

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

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

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

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

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

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:

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

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

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

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

$\pi t^3$

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

View SSAT- Upper Level Tutors

Omar
Certified Tutor

Arizona State University, Bachelors, Civil Engineering.

View SSAT- Upper Level Tutors

Carneta
Certified Tutor

Langston University, Bachelor in Arts, Theater Arts.

View SSAT- Upper Level Tutors

Pamela
Certified Tutor

University of Colorado Boulder, Bachelor of Science, International Marketing.

All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

MCAT Tutors in Dallas Fort Worth, Reading Tutors in Los Angeles, Spanish Tutors in San Francisco-Bay Area, ACT Tutors in San Diego, Chemistry Tutors in Seattle, Algebra Tutors in Boston, SSAT Tutors in Boston, Math Tutors in Houston, GRE Tutors in Atlanta, MCAT Tutors in Atlanta

Popular Courses & Classes

ACT Courses & Classes in Boston, LSAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Washington DC, ACT Courses & Classes in San Diego, SSAT Courses & Classes in San Diego, SAT Courses & Classes in Miami, GMAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Washington DC, ACT Courses & Classes in New York City, ISEE Courses & Classes in Denver

Popular Test Prep

ACT Test Prep in New York City, LSAT Test Prep in Seattle, ACT Test Prep in San Diego, GRE Test Prep in Los Angeles, GMAT Test Prep in Washington DC, LSAT Test Prep in Phoenix, LSAT Test Prep in Los Angeles, SSAT Test Prep in Washington DC, MCAT Test Prep in Miami, SSAT 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

SSAT Upper Level Math : Volume of a Three-Dimensional Figure

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #3 : Volume Of A Sphere

Example Question #11 : Know And Use The Formulas For The Volumes Of Cones, Cylinders, And Spheres: Ccss.Math.Content.8.G.C.9

Example Question #12 : Know And Use The Formulas For The Volumes Of Cones, Cylinders, And Spheres: Ccss.Math.Content.8.G.C.9

Example Question #3 : Volume Of A Three Dimensional Figure

Example Question #621 : Geometry

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

Example Question #1 : Volume Of A Three Dimensional Figure

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

All SSAT Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: