Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : High School Math

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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

Given that the radius of a sphere is 3, find the surface area.

Possible Answers:

$9\pi$

$16\pi$

$4\pi$

$12\pi$

$36\pi$

Correct answer:

$36\pi$

Explanation:

The standard equation to find the area of a sphere is

$SA=4\pi r^2$

where denotes the radius. Plug in the given radius to find the surface area.

$SA=4\pi (3)^2=4\cdot 9\cdot \pi =36\pi$

Report an Error

Example Question #6 : How To Find The Surface Area Of A Sphere

Find the surface area of the following sphere.

Sphere

Possible Answers:

$145 \pi m^2$

$144 \pi m^2$

$130 \pi m^2$

$124 \pi m^2$

$160 \pi m^2$

Correct answer:

$144 \pi m^2$

Explanation:

The formula for the surface area of a sphere is:

$SA = 4 \pi r^2$

where is the radius of the sphere.

Plugging in our values, we get:

$SA = 4 \pi (6m)^2$

$SA = 4 \pi (36m) = 144 \pi m^2$

Report an Error

Example Question #4 : How To Find The Surface Area Of A Sphere

Find the surface area of the following sphere.

Sphere

Possible Answers:

$304 \pi m^2$

$324 \pi m^2$

$334 \pi m^2$

$344 \pi m^2$

$314 \pi m^2$

Correct answer:

$324 \pi m^2$

Explanation:

The formula for the surface area of a sphere is:

$SA = 4 \pi (r^2)$

Where is the radius of the sphere

Plugging in our values, we get:

$SA = 4 \pi (9m)^2$

$SA = 324 \pi m^2$

Report an Error

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

What is the surface area of a composite figure of a cone and a sphere, both with a radius of 5 cm, if the height of the cone is 12 cm? Consider an ice cream cone as an example of the composite figure, where half of the sphere is above the edge of the cone.

Possible Answers:

$50\pi\ cm^2$

$165\pi\ cm^2$

$125\pi\ cm^2$

$65\pi\ cm^2$

$115\pi\ cm^2$

Correct answer:

$115\pi\ cm^2$

Explanation:

Calculate the slant height height of the cone using the Pythagorean Theorem. The height will be the height of the cone, the base will be the radius, and the hypotenuse will be the slant height.

s^2=r^2+h^2

$s=\sqrt{169}=13$

The surface area of the cone (excluding the base) is given by the formula $A=\pi rs$ . Plug in our values to solve.

$A_{cone}=\pi(5)(13)=65\pi\ cm^2$

The surface area of a sphere is given by $A=4\pi r^2$ but we only need half of the sphere, so the area of a hemisphere is $A=2\pi r^2$ .

$A_{hemisphere}=2\pi(5)^2=50\pi\ cm^2$

So the total surface area of the composite figure is $65\pi\ cm^2+50\pi\ cm^2=115\pi\ cm^2$ .

Report an Error

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

What is the surface area of a hemisphere with a diameter of $4\ cm$ ?

Possible Answers:

$20\pi \ cm^{2}$

$18\pi \ cm^{2}$

$8\pi \ cm^{2}$

$16\pi \ cm^{2}$

$12\pi \ cm^{2}$

Correct answer:

$12\pi \ cm^{2}$

Explanation:

A hemisphere is half of a sphere. The surface area is broken into two parts: the spherical part and the circular base.

The surface area of a sphere is given by $SA = 4\pi r^{2}$ .

So the surface area of the spherical part of a hemisphere is $SA = 2\pi r^{2}$ .

The area of the circular base is given by $A = \pi r^{2}$ . The radius to use is half the diameter, or 2 cm.

Report an Error

Example Question #11 : How To Find The Surface Area Of A Sphere

What is the surface area of a sphere with a radius of ?

Possible Answers:

$144\pi$

$24\pi$

576

$288\pi$

$576\pi$

Correct answer:

$576\pi$

Explanation:

To solve for the surface area of a sphere you must remember the formula:

First, plug the radius into the equation for :

$SA=(4)(12^{2})(\pi)$

Since $(12^{2})=144$ , the surface area is $(4)(144)(\pi)=576\pi$ .

The answer is therefore $576\pi$ .

Report an Error

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

What is the diameter of a sphere with a volume of $36\pi$ ?

Possible Answers:

Correct answer:

Explanation:

To find the diameter of a sphere we must use the equation for the volume of a sphere to find the radius which is half of the diameter.

The equation is

First we enter the volume into the equation yielding $36\pi=(\frac{4}{3})(\pi)(r^{3})$

We then divide each side by to get $36=(\frac{4}{3})(r^{3})$

We then multiply each side by to get $27=r^{3}$

We then take the cubic root of each side to solve for the radius $\sqrt[3]{27}=\sqrt[3]{r^{3}}$

The radius is r=3

We then multiply the radius by 2 to find the diameter 3*2=6

The answer for the diameter is .

Report an Error

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

The volume of a sphere is $2 8 8 \pi$ . What is the diameter?

Possible Answers:

29.4

14.7

Correct answer:

Explanation:

To find the diameter of the sphere, we need to find the radius.

The volume of a sphere is $V=\frac{4}{3}\pi r^3$ .

Plug in our given values.

$2 88\pi=\frac{4}{3}\pi r^3$

Notice that the $\pi$ 's cancel out.

$288=\frac{4}{3}r^3$

$\frac{3}{4}*288=r^3$

216=r^3

$\sqrt[3]{216}=\sqrt[3]{r^3}$

6= r

The diameter is twice the radius, so d=2r .

d=2(6)

d=12

Report an Error

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

If the surface area of a sphere is $64\pi$ , find the diameter of this sphere.

Possible Answers:

$4\sqrt{\pi }$

$4\pi$

$\sqrt{8\pi }$

Correct answer:

Explanation:

The standard equation to find the surface area of a sphere is

$SA=4\pi r^2$ where denotes the radius. Rearrange this equation in terms of :

$r=\sqrt{\frac{SA}{4\pi }}$

Substitute the given surface area into this equation and solve for the radius and then double the radius to get the diameter:

$r=\sqrt{\frac{64\Pi }{4\Pi }}=\sqrt{16}=4$

$diameter=2\cdot r=2\cdot 4=8$

Report an Error

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

Given that the volume of a sphere is $4\pi$ , find the diameter.

Possible Answers:

$2\pi \sqrt[3]{3}$

$2\sqrt[3]{4}$

$2\sqrt[3]{3\pi }$

$2\sqrt[3]{3}$

$2\sqrt[3]{4\pi }$

Correct answer:

$2\sqrt[3]{3}$

Explanation:

The standard equation to find the volume of a sphere is

$V=\frac{4}{3}\pi r^3$ where denotes the radius. Rearrange this equation in terms of :

$r=\sqrt[3]{\frac{3V}{4\pi }}$

Substitute the given volume into this equation and solve for the radius. Double the radius to find the diameter:

$r=\sqrt[3]{\frac{3V}{4\pi }}=\sqrt[3]{\frac{3\cdot 4\pi }{4\pi }}=\sqrt[3]{\frac{12\pi }{4\pi }}=\sqrt[3]{3 }$

$diameter=2\cdot r=2\sqrt[3]{3}$

Report an Error

View Tutors

Maggie
Certified Tutor

New York University, Bachelor of Science, Digital Communications and Multimedia.

View Tutors

Lucciana
Certified Tutor

Miami Dade College, Bachelor of Science, Biology, General.

View Tutors

Jeremy
Certified Tutor

University of Illinois at Chicago, Bachelor of Science, Physics.

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

SAT Tutors in Atlanta, Biology Tutors in Houston, Calculus Tutors in San Diego, Calculus Tutors in Denver, English Tutors in Los Angeles, SSAT Tutors in Los Angeles, Algebra Tutors in Boston, GRE Tutors in San Francisco-Bay Area, ISEE Tutors in New York City, Algebra Tutors in New York City

Popular Courses & Classes

Spanish Courses & Classes in San Diego, GMAT Courses & Classes in Atlanta, ACT Courses & Classes in Philadelphia, SAT Courses & Classes in Chicago, ISEE Courses & Classes in Seattle, GMAT Courses & Classes in Denver, LSAT Courses & Classes in Miami, SSAT Courses & Classes in Chicago, ACT Courses & Classes in San Diego, GMAT Courses & Classes in New York City

Popular Test Prep

GRE Test Prep in Denver, GMAT Test Prep in Miami, ISEE Test Prep in Denver, GRE Test Prep in Phoenix, MCAT Test Prep in Los Angeles, LSAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Denver, SSAT Test Prep in Atlanta, LSAT Test Prep in Phoenix, SAT Test Prep in San Diego

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

High School Math : High School Math

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

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

Example Question #6 : How To Find The Surface Area Of A Sphere

Example Question #4 : How To Find The Surface Area Of A Sphere

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

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

Example Question #11 : How To Find The Surface Area Of A Sphere

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

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

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

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

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: