Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : How to find the surface area of a sphere

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

← Previous 1 2 Next →

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

What is the surface area of a sphere with a radius of 15?

Possible Answers:

$900\pi$

$225\pi$

$450\pi$

$665\pi$

Correct answer:

$900\pi$

Explanation:

To solve for the surface area of a sphere you must use the equation

First, plug in 15 for and square it

$SA=4(15^2)\pi$

Multiply by 4 and to get

$900\pi=225(4)(\pi)$

The answer is $900\pi$ .

Report an Error

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

What is the surface area of a sphere whise radius is r=1.5cm .

Possible Answers:

$9\pi cm^{2}$

$\dpi{100} 18\pi cm^{2}$

Not enough information to solve

$\dpi{100} 4.5\pi cm^{2}$

$\dpi{100} 12.14 cm^{2}$

Correct answer:

$9\pi cm^{2}$

Explanation:

The surface area of a sphere is found by the formula $SA=4\pi r^{2}$ using the given radius of r=1.5cm .

$SA=4\pi (1.5cm)^{2}$

$SA=4*\pi*2.25cm^{2}$

$\rightarrow 9\pi cm^{2}$

Report an Error

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

Find the surface area of a sphere whose diameter is $D=\pi$ .

Possible Answers:

$\dpi{100} 2\pi^{2}$

37.7

$\dpi{100} 4\pi^{2}$

$\pi ^{3}$

$\dpi{100} 2\pi^{3}$

Correct answer:

$\pi ^{3}$

Explanation:

The surface area of a sphere is found by the formula $SA=4\pi r^{2}$ . We need to first convert the given diameter of $D=\pi$ to the sphere's radius.

D=2r

$\pi =2r$

$r=\pi/2$

Now, we can solve for surface area.

$\dpi{100} \dpi{100} SA=4\pi \left ( \frac{\pi }{2}\right)^{2}$

$=4\pi \cdot \frac{\pi^{2} }{4}$

$\dpi{100} \rightarrow \pi^{3}$

Report an Error

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

To the nearest tenth of a square centimeter, give the surface area of a sphere with volume 1,000 cubic centimeters.

Possible Answers:

$314.2 \textrm{ cm}^{2}$

$333.3 \textrm{ cm}^{2}$

$120.9 \textrm{ cm}^{2}$

$483.6 \textrm{ cm}^{2}$

$708.3 \textrm{ cm}^{2}$

Correct answer:

$483.6 \textrm{ cm}^{2}$

Explanation:

The volume of a sphere in terms of its radius is

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

Substitute V = 1,000 and solve for :

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

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

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

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

$r=\sqrt[3]{ \frac{3,000}{4\pi }} \approx 6.20 \textrm{ cm }$

Substitute for in the formula for the surface area of a sphere:

$A = 4\pi r^2 \approx 4 \cdot \pi \cdot 6.20 ^2 \approx 483.6 \textrm{ cm}^{2}$

Report an Error

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

Find the surface area of a sphere with a radius of .

Possible Answers:

$42\Pi$

$4\Pi$

$16\Pi$

$36\Pi$

$64\Pi$

Correct answer:

$64\Pi$

Explanation:

The standard equation to find the area of a sphere is $4\Pi r^2$ .

Substitute the given radius into the standard equation to get the answer:

$4\Pi (4)^2=4\Pi (16)=64\Pi$

Report an Error

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

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

Possible Answers:

$4\pi$

$36\pi$

$12\pi$

$9\pi$

$16\pi$

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 #7 : How To Find The Surface Area Of A Sphere

Find the surface area of the following sphere.

Sphere

Possible Answers:

$145 \pi m^2$

$160 \pi m^2$

$124 \pi m^2$

$130 \pi m^2$

$144 \pi m^2$

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 #8 : How To Find The Surface Area Of A Sphere

Find the surface area of the following sphere.

Sphere

Possible Answers:

$304 \pi m^2$

$324 \pi m^2$

$314 \pi m^2$

$334 \pi m^2$

$344 \pi m^2$

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 #1 : 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:

$115\pi\ cm^2$

$50\pi\ cm^2$

$65\pi\ cm^2$

$125\pi\ cm^2$

$165\pi\ cm^2$

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 #8 : 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:

$16\pi \ cm^{2}$

$8\pi \ cm^{2}$

$12\pi \ cm^{2}$

$20\pi \ cm^{2}$

$18\pi \ cm^{2}$

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

← Previous 1 2 Next →

View Tutors

Annette
Certified Tutor

University of Maryland-University College, Bachelor of Science, Computer and Information Sciences, General. University of Mar...

View Tutors

Farhana
Certified Tutor

Albany College of Pharmacy and Health Sciences, Bachelor of Science, Public Health.

View Tutors

Anna
Certified Tutor

All High School Math Resources

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

Popular Subjects

LSAT Tutors in Boston, Spanish Tutors in Boston, Calculus Tutors in Philadelphia, Computer Science Tutors in Washington DC, French Tutors in Washington DC, Physics Tutors in Washington DC, Algebra Tutors in Boston, LSAT Tutors in Atlanta, English Tutors in Atlanta, Computer Science Tutors in Seattle

Popular Courses & Classes

Spanish Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Washington DC, ISEE Courses & Classes in Chicago, GMAT Courses & Classes in Phoenix, SAT Courses & Classes in Miami, Spanish Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Philadelphia, GRE Courses & Classes in Miami, MCAT Courses & Classes in Miami, SSAT Courses & Classes in Boston

Popular Test Prep

ISEE Test Prep in Miami, GMAT Test Prep in Philadelphia, ACT Test Prep in Los Angeles, LSAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Boston, GMAT Test Prep in Houston, SSAT Test Prep in Denver, ACT Test Prep in Seattle, LSAT Test Prep in New York City, GMAT 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

High School Math : How to find the surface area of a sphere

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

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

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

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 #7 : How To Find The Surface Area Of A Sphere

Example Question #8 : How To Find The Surface Area Of A Sphere

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

Example Question #8 : How To Find The Surface Area 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: