Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Math : Spheres

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

Create An Account

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Spheres

There is a perfectly spherical weather balloon with a surface area of $900 \pi ft^2$ , what is its diameter?

Possible Answers:

30ft

15ft

25 ft

22.5ft

Correct answer:

30ft

Explanation:

There is a perfectly spherical weather balloon with a surface area of $900 \pi ft^2$ , what is its diameter?

Begin with the formula for surface area of a sphere:

$SA_{sphere}=4 \pi r^2$

Now, set it equal to the given surface area and solve for r:

$900 \pi ft^2=4 \pi r^2$

First divide both sides by $4\pi$ .

225ft^2=r^2

Then square root both sides to get our radius:

r=15ft

Now, because the question is asking for our diameter and not our radius, we need to double our radius to get our answer:

d=2r=2*15ft=30 ft

Report an Error

Example Question #2 : Spheres

A wooden ball has a surface area of $900\pi m^2$ .

What is its radius?

Possible Answers:

Cannot be determined from the information provided

25 m

12.5m

15m

Correct answer:

15m

Explanation:

A wooden ball has a surface area of $900\pi m^2$ .

What is its radius?

Begin with the formula for surface area of a sphere:

$SA_{sphere}=4\pi r^2$

Now, plug in our surface area and solve with algebra:

$900 \pi m^2=4\pi r^2$

Get rid of the pi

900 m^2=4 r^2

Divide by 4

225 m^2= r^2

Square root both sides to get our answer:

r=15m

Report an Error

Example Question #3 : Spheres

There is a perfectly spherical weather balloon with a surface area of $900 \pi ft^2$ , what is its radius?

Possible Answers:

15 ft

25 ft

225 ft

45 ft

Correct answer:

15 ft

Explanation:

There is a perfectly spherical weather balloon with a surface area of $900 \pi ft^2$ , what is its radius?

Begin with the formula for surface area of a sphere:

$SA_{sphere}=4 \pi r^2$

Now, set it equal to the given surface area and solve for r:

$900 \pi ft^2=4 \pi r^2$

First divide both sides by $4\pi$ .

225ft^2=r^2

Then square root both sides to get our answer:

r=15ft

Report an Error

Example Question #1 : Volume Of A Sphere

In terms of $\pi$ , give the volume, in cubic inches, of a spherical water tank with a diameter of 20 feet.

Possible Answers:

$230,400 \pi\textrm{ in}^{3}$

$2,304,000 \pi \textrm{ in}^{3}$

$18,432,000\pi\textrm{ in}^{3}$

$307,200\pi\textrm{ in}^{3}$

$57,600 \pi\textrm{ in}^{3}$

Correct answer:

$2,304,000 \pi \textrm{ in}^{3}$

Explanation:

20 feet = $20 \times 12 = 240$ inches, the diameter of the tank; half of this, or 120 inches, is the radius. Set r = 120 , substitute in the volume formula, and solve for :

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

$V = \frac{4}{3} \pi \cdot 120^{3}$

$V = \frac{4}{3} \pi \cdot 1,728,000$

$V = 2,304,000 \pi$ cubic inches

Report an Error

Example Question #71 : Solid Geometry

A sphere has diameter 3 meters. Give its volume in cubic centimeters (leave in terms of $\pi$ ).

Possible Answers:

$36,000,000\pi \textrm{ cm}^{3}$

$1,125,000\pi \textrm{ cm}^{3}$

$4,500,000\pi \textrm{ cm}^{3}$

$3,375,000\pi \textrm{ cm}^{3}$

$27,000,000\pi \textrm{ cm}^{3}$

Correct answer:

$4,500,000\pi \textrm{ cm}^{3}$

Explanation:

The diameter of 3 meters is equal to $3 \times 100 = 300$ centimeters; the radius is half this, or 150 centimeters. Substitute r = 150 in the volume formula:

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

$V= \frac{4}{3} \cdot \pi \cdot 150^{3}$

$V= \frac{4}{3} \cdot 150 \cdot 150 \cdot 150\cdot \pi$

$V= 4,500,000\pi$ cubic centimeters

Report an Error

Example Question #1 : Spheres

A spherical buoy has a radius of 5 meters. What is the volume of the buoy?

Possible Answers:

$165 \pi m^3$

$16\frac{2}{3}\pi m^3$

$166\frac{2}{3}\pi m^3$

$166\frac{2}{3} m^3$

Correct answer:

$166\frac{2}{3}\pi m^3$

Explanation:

A spherical buoy has a radius of 5 meters. What is the volume of the buoy?

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

$V_{sphere}=\frac{4}{3}\pi r^3$

All we have to do is plug in 5 meters and simplify:

$V_{sphere}=\frac{4}{3}\pi (5m)^3=\frac{4}{3}\pi*125m^3=166\frac{2}{3}\pi m^3$

Report an Error

Example Question #2 : Spheres

You have a ball with a radius of 12 cm, what is its volume?

Possible Answers:

$144 \pi cm^3$

$192 \pi cm^3$

$404 \pi cm^3$

$2304 \pi cm^3$

Correct answer:

$2304 \pi cm^3$

Explanation:

You have a ball with a radius of 12 cm, what is its volume?

The volume of a sphere can be found via the following formula:

$V_{sphere}=\frac{4}{3}\pi r^3$

We know our radius, so all we need to do is plug in and simplify:

$V_{sphere}=\frac{4}{3}\pi (12cm)^3=2304 \pi cm^3$

So we have our answer:

$2304 \pi cm^3$

Report an Error

Example Question #3 : Spheres

You have a wooden ball which you are going to paint. If the radius is 12 inches, what is the volume of the ball?

Possible Answers:

$576 \pi in^3$

$2304\pi in^3$

$1728\pi in^3$

2304 in^3

Correct answer:

$2304\pi in^3$

Explanation:

You have a wooden ball which you are going to paint. If the radius is 12 inches, what is the volume of the ball?

Alright, let's begin with the volume of a sphere formula:

$V_{sphere}=\frac{4}{3}\pi r^3$

Now, plug in 12 and simplify:

$V_{sphere}=\frac{4}{3}\pi(12in)^3=\frac{4}{3}\pi*1728in^3=2304\pi in^3$

Report an Error

Example Question #4 : Spheres

Find the volume of a sphere with a diameter of 6cm.

Possible Answers:

$42\pi \text{ cm}^3$

$36\pi \text{ cm}^3$

$108\pi \text{ cm}^3$

$24\pi \text{ cm}^3$

$216\pi \text{ cm}^3$

Correct answer:

$36\pi \text{ cm}^3$

Explanation:

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

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

where r is the radius of the sphere.

Now, we know the diameter of the sphere is 6cm. We also know that the diameter is two times the radius. Therefore, the radius is 3cm.

Knowing this, we can substitute into the formula. We get

$V = \frac{4}{3} \cdot \pi \cdot (3\text{cm})^3$

$V = \frac{4}{3} \cdot \pi \cdot 3\text{cm} \cdot 3\text{cm} \cdot 3\text{cm}$

$V = \frac{4}{3} \cdot \pi \cdot 27\text{cm}^3$

Now, before we continue, we can simplify. The 3 and the 27 can both be divided by 3. We get

$V = \frac{4}{1} \cdot \pi \cdot 9\text{cm}^3$

$V = 4 \cdot \pi \cdot 9\text{cm}^3$

$V = 36\pi \text{ cm}^3$

Report an Error

Example Question #7 : How To Find The Volume Of A Sphere

Find the volume of a sphere with a diameter of 12in.

Possible Answers:

$96\pi \text{ in}^3$

$288\pi \text{ in}^3$

$144\pi \text{ in}^3$

$200\pi \text{ in}^3$

$256\pi \text{ in}^3$

Correct answer:

$288\pi \text{ in}^3$

Explanation:

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

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

where r is the radius of the sphere.

Now, we know the diameter of the sphere is 12in. We also know the diameter is two times the radius. Therefore, the radius is 6in.

Knowing this, we can substitute into the formula. We get

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

$V = \frac{4}{3} \cdot \pi \cdot 6\text{in} \cdot 6\text{in} \cdot 6\text{in}$

Now, we can simplify before we multiply to make things easier. The 3 and a 6 can both be divided by 3. So, we get

$V = \frac{4}{1} \cdot \pi \cdot 2\text{in} \cdot 6\text{in} \cdot 6\text{in}$

$V = 4 \cdot \pi \cdot 72\text{in}^3$

$V = 288\pi \text{ in}^3$

Report an Error

View Tutors

Gabby
Certified Tutor

University of Oregon, Bachelor in Arts, Journalism. University of Oregon, Current Grad Student, Communication, General.

View Tutors

Joseph
Certified Tutor

Bank Street College of Education , Master's/Graduate, Early Childhood and Childhood General Education.

View Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in Boston, GMAT Tutors in Dallas Fort Worth, GRE Tutors in New York City, MCAT Tutors in Denver, Reading Tutors in Atlanta, Computer Science Tutors in Seattle, GMAT Tutors in Houston, Physics Tutors in San Francisco-Bay Area, Math Tutors in Boston, Chemistry Tutors in Seattle

Popular Courses & Classes

Spanish Courses & Classes in Los Angeles, GRE Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Seattle, ISEE Courses & Classes in Miami, ACT Courses & Classes in San Diego, ACT Courses & Classes in Seattle, MCAT Courses & Classes in Los Angeles, SAT Courses & Classes in Washington DC, GMAT Courses & Classes in Denver, Spanish Courses & Classes in Denver

Popular Test Prep

ACT Test Prep in Seattle, GRE Test Prep in Los Angeles, GRE Test Prep in Miami, GRE Test Prep in New York City, SAT Test Prep in Chicago, GMAT Test Prep in Seattle, GRE Test Prep in Phoenix, SAT Test Prep in Atlanta, ACT Test Prep in Philadelphia, MCAT Test Prep in San Francisco-Bay Area

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

ISEE Upper Level Math : Spheres

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 : Spheres

Example Question #2 : Spheres

Example Question #3 : Spheres

Example Question #1 : Volume Of A Sphere

Example Question #71 : Solid Geometry

Example Question #1 : Spheres

Example Question #2 : Spheres

Example Question #3 : Spheres

Example Question #4 : Spheres

Example Question #7 : How To Find The Volume Of A Sphere

All ISEE Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: