We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SAT II Math II : 3-Dimensional Geometry

Study concepts, example questions & explanations for SAT II Math II

Create An Account

All SAT II Math II Resources

2 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 Next →

Example Question #81 : Geometry

Find the volume of a sphere with a diameter of 10.

Possible Answers:

$166.67\pi$

$33.33\pi$

$25\pi$

$1333.33\pi$

$100\pi$

Correct answer:

$166.67\pi$

Explanation:

The surface area of a sphere is found using the formula $A=\frac{4}{3}\pi r^3$ . We are given the diameter of the circle and so we have to use it to find the radius (r).

$Radius=\frac{Diameter}{2}=\frac{10}{2}=5$

Plug r into the formula to find the surface area

$A=\frac{4}{3}\pi 5^3=\frac{4}{3}\pi 125=166.67\pi$

Report an Error

Example Question #391 : Sat Subject Test In Math Ii

Determine the volume of the cube with a side length of 3x^2 .

Possible Answers:

3x^8

9x^6

3x^6

27x^8

27x^6

Correct answer:

27x^6

Explanation:

Write the formula for the volume of a cube.

V = s^3

Substitute the length into the formula.

V = (3x^2)^3=(3x^2)(3x^2)(3x^2) = 27x^6

The volume is: 27x^6

Report an Error

Example Question #91 : Geometry

Billy has a ice cream cone that consists of a cone and hemisphere. Suppose the cone has a height of 4 inches, and the radius of the hemisphere is 2 inches. Assuming that the combined shape is not irregular, what is the total volume?

Possible Answers:

$\frac{16}{3}\pi$

$\frac{64}{9}\pi$

$\frac{64}{3}\pi$

$\frac{8}{3}\pi$

$\frac{32}{3}\pi$

Correct answer:

$\frac{32}{3}\pi$

Explanation:

Write the volume for a cone.

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

Substitute the radius and height. The radius is 2.

$V_{cone } = \frac{1}{3}\pi (2)^2 (4) = \frac{16}{3}\pi$

Write the volume for a hemisphere. This should be half the volume of the full sphere.

$V_{hemisphere} = \frac{1}{2}[ \frac{4}{3}\pi r^3] = \frac{2}{3}\pi r^3$

Substitute the radius.

$V_{hemisphere}= \frac{2}{3}\pi (2)^3 = \frac{16}{3}\pi$

Add the volumes of the cone and hemisphere to determine the total volume.

$\frac{16}{3}\pi+\frac{16}{3}\pi$

The answer is: $\frac{32}{3}\pi$

Report an Error

Example Question #92 : Geometry

Find the volume of a sphere with a diameter of $\frac{\sqrt[3]{2}}{2}$ .

Possible Answers:

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

$\frac{1}{6}\pi$

$\frac{1}{24}\pi$

$\frac{1}{12}\pi$

$\frac{1}{9}\pi$

Correct answer:

$\frac{1}{24}\pi$

Explanation:

Divide the diameter by two to get the radius. This is also the same as multiplying the diameter by one-half.

$r =\frac{\sqrt[3]{2}}{2} \cdot \frac{1}{2} = \frac{\sqrt[3]{2}}{4}$

Write the formula for the volume of the sphere.

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

Substitute the radius.

$V=\frac{4}{3}\pi ( \frac{\sqrt[3]{2}}{4})^3$

Simplify the terms.

$\frac{4}{3}\pi ( \frac{\sqrt[3]{2}}{4})^3 = \frac{4}{3}\pi ( \frac{\sqrt[3]{2}}{4})( \frac{\sqrt[3]{2}}{4})( \frac{\sqrt[3]{2}}{4}) = \frac{2}{3(4)(4)}\pi$

The answer is: $\frac{1}{24}\pi$

Report an Error

Example Question #11 : 3 Dimensional Geometry

If the side of a cube is 3x^3 , what must be the volume?

Possible Answers:

9x^9

$27x^{27}$

27x^6

27x^9

27x^3

Correct answer:

27x^9

Explanation:

Write the formula for the volume of a cube.

V =s^3

Substitute the side length. When we are multiplying common bases with exponents, we are adding the exponents instead.

V =(3x^3)^3 = (3x^3)(3x^3)(3x^3) = 27x^9

The answer is: 27x^9

Report an Error

Example Question #11 : 3 Dimensional Geometry

Determine the volume of a cube if the side length is $2\sqrt6$ .

Possible Answers:

$24\sqrt3$

$72\sqrt3$

$8\sqrt6$

$48\sqrt6$

Correct answer:

$48\sqrt6$

Explanation:

Write the formula for the volume of a cube.

V= s^3

Substitute the side length into the equation.

$V= (2\sqrt6)^3 = (2\sqrt6)(2\sqrt6)(2\sqrt6) = 8\cdot 6\cdot \sqrt6$

The answer is: $48\sqrt6$

Report an Error

Example Question #11 : 3 Dimensional Geometry

The radius and the height of a cylinder are equal. If the volume of the cylinder is , what is the diameter of the cylinder?

Possible Answers:

3.21

1.77

2.95

1.61

Correct answer:

3.21

Explanation:

Recall how to find the volume of a cylinder:

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

Since we know that the radius and the height are equal, we can rewrite the equation:

$\text{Volume}=\pi r^2 (r)=\pi r^3$

Using the given volume, find the length of the radius.

$13=\pi r^3$

r^3=4.138

r=1.605

Since the question asks you to find the diameter, multiply the radius by two.

d=3.21

Report an Error

Example Question #11 : Volume

Determine the volume of the cube if the side lengths are $\frac{2}{5}$ .

Possible Answers:

$\frac{8}{15}$

$\frac{6}{125}$

$\frac{6}{5}$

$\frac{8}{125}$

Correct answer:

$\frac{8}{125}$

Explanation:

The volume of a cube is: V =LWH

Substitute the dimensions.

$V =(\frac{2}{5})(\frac{2}{5})(\frac{2}{5}) = \frac{8}{125}$

The answer is: $\frac{8}{125}$

Report an Error

Example Question #11 : 3 Dimensional Geometry

Determine the volume of a sphere with a diameter of 6.

Possible Answers:

$296\pi$

$24\pi$

$36\pi$

$396\pi$

$48\pi$

Correct answer:

$36\pi$

Explanation:

The radius is half the diameter, which is three.

Write the formula for the volume of a sphere.

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

Substitute the radius.

$V=\frac{4}{3}\pi (3)^3 = 36\pi$

The answer is: $36\pi$

Report an Error

Example Question #11 : Volume

Find the volume of a sphere with a radius of $2\pi^4$ .

Possible Answers:

$\frac{16}{3}\pi ^{12}$

$\frac{4}{3}\pi ^{13}$

$\frac{32}{3}\pi ^{13}$

$\frac{16}{3}\pi ^{13}$

$8\pi ^{13}$

Correct answer:

$\frac{32}{3}\pi ^{13}$

Explanation:

Write the formula for the sphere.

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

Substitute the radius.

$V=\frac{4}{3} \pi (2\pi^4)^3 = \frac{4}{3} \pi (2\pi^4)(2\pi^4)(2\pi^4)$

The answer is: $\frac{32}{3}\pi ^{13}$

Report an Error

← Previous 1 2 3 4 5 Next →

View SAT Subject Test in Mathematics Level 2 Tutors

Luu Chi Hieu
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Computer Science.

View SAT Subject Test in Mathematics Level 2 Tutors

Antonia
Certified Tutor

University of Michigan-Ann Arbor, Bachelor of Engineering, Nuclear Engineering. University of Wisconsin-Madison, Current Grad...

View SAT Subject Test in Mathematics Level 2 Tutors

Reuben
Certified Tutor

University of Alberta, Bachelor of Science, Mathematics.

All SAT II Math II Resources

2 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Computer Science Tutors in Philadelphia, Computer Science Tutors in Chicago, LSAT Tutors in Denver, LSAT Tutors in Seattle, French Tutors in Houston, ISEE Tutors in San Diego, Chemistry Tutors in Phoenix, ISEE Tutors in Denver, LSAT Tutors in Los Angeles, ISEE Tutors in Washington DC

Popular Courses & Classes

Spanish Courses & Classes in Washington DC, ACT Courses & Classes in Chicago, Spanish Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Houston, GMAT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Atlanta, ACT Courses & Classes in Boston, ACT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Los Angeles

Popular Test Prep

ISEE Test Prep in Los Angeles, SAT Test Prep in Miami, LSAT Test Prep in Los Angeles, GRE Test Prep in Seattle, SSAT Test Prep in Seattle, LSAT Test Prep in Seattle, SAT Test Prep in Dallas Fort Worth, LSAT Test Prep in San Francisco-Bay Area, ACT Test Prep in San Diego, SAT 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

SAT II Math II : 3-Dimensional Geometry

Study concepts, example questions & explanations for SAT II Math II

All SAT II Math II Resources

Example Questions

Example Question #81 : Geometry

Example Question #391 : Sat Subject Test In Math Ii

Example Question #91 : Geometry

Example Question #92 : Geometry

Example Question #11 : 3 Dimensional Geometry

Example Question #11 : 3 Dimensional Geometry

Example Question #11 : 3 Dimensional Geometry

Example Question #11 : Volume

Example Question #11 : 3 Dimensional Geometry

Example Question #11 : Volume

All SAT II Math II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: