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 Surface Area Of A Sphere

What is the surface area of a sphere that has a diameter of eight inches? Reduce any fractions in your answer and leave your answer in terms of $\pi$ .

Possible Answers:

$64 \pi inches^3$

$256 \pi inches^2$

$64\pi inches^2$

$256 \pi inches^3$

$\frac{2048}{3} \pi inches^3$

Correct answer:

$64\pi inches^2$

Explanation:

To find the volume of a sphere area of a sphere plug the radius into the following formula given by :

$SA = 4\pi r^2$ .

To find the radius given the diameter, divide the diameter by 2.

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

$r=\frac{8}{2}=4$
Thus:
$SA = 4\pi 4^2 = 64 \pi inches^2$

Report an Error

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

What is the surface area of a sphere, in inches, that has a surface area equal to its volume? Leave your answer in terms of $\pi$ .

Possible Answers:

$108\pi in^2$

$9\pi in^2$

$36\pi in^3$

$36\pi in^2$

$27\pi in^2$

Correct answer:

$36\pi in^2$

Explanation:

To find the radius of a sphere that has a volume equal to it's surface area, begin by setting the volume and surface area formulas for a sphere equal to each other and solving for the radius:
$\\\frac{4}{3}\pi r^3 = 4\pi r^2 \newline \newline \frac{4}{3}r^3 = 4r^2 \newline \newline 4r^3 = 12r^2 \newline r^3 = 3r^2 \newline r = 3$

Next we plug the answer for our radius into the formula for the surface area:

$4\pi 3^2 = 36\pi in^2$ , remember to check the units.

Report an Error

Example Question #3 : How To Find The Surface Area Of A Sphere

Find the surface area of a sphere whose radius is .

Possible Answers:

$4\pi$

$108\pi$

$36\pi$

$12\pi$

Correct answer:

$36\pi$

Explanation:

To solve, simply remember the following formula:

$SA=4\pi{r^2}=4*\pi*3^2=36\pi$

Report an Error

Example Question #733 : Geometry

Find the surface area of a sphere whose radius is . Thus,

Possible Answers:

$48\pi$

$32\pi$

$36\pi$

$12\pi$

Correct answer:

$36\pi$

Explanation:

To find surface area, simply use the formula. Thus,

$SA=4\pi{r^2}=4\cdot\pi\cdot3^2=4\cdot\pi\cdot9=36\pi$

Report an Error

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

Find the surface area of a sphere whose side diameter is .

Possible Answers:

$8\pi$

$4\pi$

$2\pi$

$3\pi$

Correct answer:

$4\pi$

Explanation:

To solve, simply use the following formula for the surface area of a circle. Thus,

$SA=4\pi{r^2}=4*\pi*1^2=4\pi$

Report an Error

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

For a sphere the volume is given by V = (4/3)πr³ and the surface area is given by A = 4πr². If the sphere has a surface area of 256π, what is the volume?

Possible Answers:

750π

615π

300π

683π

Correct answer:

683π

Explanation:

Given the surface area, we can solve for the radius and then solve for the volume.

4πr² = 256π

4r² = 256

r² = 64

r = 8

Now solve the volume equation, substituting for r:

V = (4/3)π(8)³

V = (4/3)π*512

V = (2048/3)π

V = 683π

Report an Error

Example Question #1 : Spheres

The specifications of an official NBA basketball are that it must be 29.5 inches in circumference and weigh 22 ounces. What is the approximate volume of the basketball? Remember that the volume of a sphere is calculated by V=(4πr³)/3

Possible Answers:

138.43 cu.in.

8557.46 cu.in.

3468.05 cu.in.

92.48 cu.in.

434.19 cu.in.

Correct answer:

434.19 cu.in.

Explanation:

To find your answer, we would use the formula: C=2πr. We are given that C = 29.5. Thus we can plug in to get [29.5]=2πr and then multiply 2π to get 29.5=(6.28)r. Lastly, we divide both sides by 6.28 to get 4.70=r. Then we would plug into the formula for volume V=(4π〖(4.7)〗³) / 3 (The information given of 22 ounces is useless)

Report an Error

Example Question #11 : Spheres

The radius of a sphere is . What is the approximate volume of this sphere?

Possible Answers:

$138\pi$

$300\pi$

$516\pi$

$20\pi$

$288\pi$

Correct answer:

$288\pi$

Explanation:

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

$V=\frac{4}{3}\pi(6)^3$

$V=\frac{4}{3}\pi(216)$

$V=288\pi$

Report an Error

Example Question #12 : Spheres

A cube has a side dimension of 4. A sphere has a radius of 3. What is the volume of the two combined, if the cube is balanced on top of the sphere?

Possible Answers:

$16 + 36\pi$

$64 + 6\pi$

$16 + 6\pi$

$4 + 36\pi$

$64 + 36\pi$

Correct answer:

$64 + 36\pi$

Explanation:

$V_{cube}=(\text{side})^3=(4)^3=64$

$V_{sphere}=\frac{4}{3}\pi r^3=\frac{4}{3}\pi(3^3)=\frac{4}{3}\pi(27)=36\pi$

$V_{total}=64+36\pi$

Report an Error

Example Question #1 : Spheres

What is the volume of a sphere with a diameter of 6 in?

Possible Answers:

$36\pi\ in^{3}$

$288\pi\ in^{3}$

$108\pi\ in^{3}$

$216\pi\ in^{3}$

$72\pi\ in^{3}$

Correct answer:

$36\pi\ in^{3}$

Explanation:

The formula for the volume of a sphere is:

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

where = radius. The diameter is 6 in, so the radius will be 3 in.

Report an Error

View ACT Math Tutors

Armon
Certified Tutor

Loyola University-Chicago, Bachelor of Science, Biology, General. Columbia College-Chicago, Bachelor of Science, Graphic Desi...

View ACT Math Tutors

Kaitlyn
Certified Tutor

Fairfield University, Bachelor of Science, Biology, General. NUI Galway Ireland, Master of Science, Neuroscience.

View ACT Math Tutors

Gary
Certified Tutor

SUNY at Albany, Bachelor of Science, Economics. Pace University-New York, Masters in Business Administration, Analysis and Fu...

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 San Diego, SSAT Courses & Classes in Washington DC, ACT Courses & Classes in Washington DC, ACT Courses & Classes in Boston, SAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Denver, LSAT Courses & Classes in Washington DC, ISEE Courses & Classes in Houston, SAT Courses & Classes in Washington DC, ISEE Courses & Classes in Atlanta

Popular Test Prep

SAT Test Prep in Dallas Fort Worth, SAT Test Prep in Los Angeles, ISEE Test Prep in Dallas Fort Worth, GRE Test Prep in Washington DC, ACT Test Prep in San Diego, MCAT Test Prep in Los Angeles, SSAT Test Prep in Chicago, SSAT Test Prep in San Diego, LSAT Test Prep in Seattle, ACT Test Prep in Miami

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 Surface Area Of A Sphere

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

Example Question #3 : How To Find The Surface Area Of A Sphere

Example Question #733 : Geometry

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

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

Example Question #1 : Spheres

Example Question #11 : Spheres

Example Question #12 : Spheres

Example Question #1 : Spheres

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: