Call Now to Set Up Tutoring:

(888) 888-0446

Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

Create An Account

All Basic Geometry Resources

9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #91 : How To Find Circumference

Find the circumference of the circle if the lengths of the legs of the inscribed isosceles triangle are .

Possible Answers:

$3\sqrt2\pi$

$9\sqrt2\pi$

$\sqrt3\pi$

$3\pi$

Correct answer:

$3\sqrt2\pi$

Explanation:

Notice that the hypotenuse of the triangle in the figure is also the diameter of the circle.

Use the Pythagorean theorem to find the length of the hypotenuse.

$\text{Hypotenuse}^2=\text{leg}^2+\text{leg}^2$

$\text{Hypotenuse}^2=2(\text{leg}^2)$

$\text{Hypotenuse}=\sqrt{2(\text{leg}^2)}=\text{leg}\sqrt2$

Substitute in the length of triangle’s legs to find the missing length of the hypotenuse.

$\text{Hypotenuse}=3\sqrt2$

Now, recall that the hypotenuse of the triangle and the diameter of the circle are the same:

$\text{Hypotenuse}=\text{Diameter}=3\sqrt2$

Now, recall how to find the circumference of a circle:

$\text{Circumference}=\text{Diameter}\times\pi$

Substitute in the value for the diameter to find the circumference of the circle.

$\text{Circumference}=3\sqrt2\pi$

Report an Error

Example Question #291 : Circles

Find the circumference of the circle if the lengths of the legs of the inscribed isosceles triangle are .

Possible Answers:

$2\pi$

$2\sqrt2\pi$

$8\sqrt2\pi$

$\sqrt2\pi$

Correct answer:

$2\sqrt2\pi$

Explanation:

Notice that the hypotenuse of the triangle in the figure is also the diameter of the circle.

Use the Pythagorean theorem to find the length of the hypotenuse.

$\text{Hypotenuse}^2=\text{leg}^2+\text{leg}^2$

$\text{Hypotenuse}^2=2(\text{leg}^2)$

$\text{Hypotenuse}=\sqrt{2(\text{leg}^2)}=\text{leg}\sqrt2$

Substitute in the length of triangle’s legs to find the missing length of the hypotenuse.

$\text{Hypotenuse}=2\sqrt2$

Now, recall that the hypotenuse of the triangle and the diameter of the circle are the same:

$\text{Hypotenuse}=\text{Diameter}=2\sqrt2$

Now, recall how to find the circumference of a circle:

$\text{Circumference}=\text{Diameter}\times\pi$

Substitute in the value for the diameter to find the circumference of the circle.

$\text{Circumference}=2\sqrt2\pi$

Report an Error

Example Question #291 : Plane Geometry

Find the circumference of a circle whose radius is 5.

Possible Answers:

$10\pi$

$25\pi$

Correct answer:

$10\pi$

Explanation:

The circumference of a circle is the length of the outside curved line which incloses the circle.

To solve, simply use the formula for the circumference of a circle.

Thus,

r=5

$c=2\pi{r}=2*\pi*5=10\pi$

Report an Error

Example Question #292 : Plane Geometry

Find the circumference of a circle given the radius is 7.

Possible Answers:

$49\pi$

$14\pi$

Correct answer:

$14\pi$

Explanation:

To solve, simply use the formula for the circumference of a circle. Thus,

$C=2\pi{r}=2*\pi*7=14\pi$

Another way to similarly solve this problem is to remember that circumference is just pi times the diameter. To find the diameter, remember "di" means two, thus two radii. So, if you multiply the radius by 2, then you have the diameter. Then, just multiply by pi.

Report an Error

Example Question #101 : How To Find Circumference

A circle has a radius of 3.5 cm . What is the circumference of the circle?

Possible Answers:

$12.25\pi cm$

$3.5\pi cm$

$49\pi cm$

$\pi cm$

$7\pi cm$

Correct answer:

$7\pi cm$

Explanation:

The formula to find the circumference of a cirlce using the radius is:

$C=2\pi r$

The radius is 3.5 cm , so we plug that into the formula:

$C=2\pi (3.5)$

$C=7\pi cm$

Report an Error

Example Question #293 : Plane Geometry

What is the circumference of a circle with a radius of $5.2\textup{ in}$ ?

Possible Answers:

$22.8\textup{ in}$

$49.3\textup{ in}$

$32.7\textup{ in}$

$10.4\textup{ in}$

$16.3\textup{ in}$

(Round your answer to the nearest tenth.)

Correct answer:

$32.7\textup{ in}$

Explanation:

The circumference is given by the formula:

$C=2\pi r$

where is the radius.

$2\pi (5.2)=32.7\ in$

Report an Error

Example Question #102 : How To Find Circumference

A vinyl record uncovered from your grandfather's attic is circular in shape and has a diameter of {10}'' . What is the circumferance of the record rounded to the nearest tenth?

Possible Answers:

31.4{}''

{15.7}''

{23.7}''

{30.2}''

{62.8}''

Correct answer:

31.4{}''

Explanation:

To find the circumference, we want to use the formula for calculating circumference:

$\\circ.=\pi\cdot d\\circ.=3.14159\cdot10{}''\\circ.\approx31.4{}''$

Report an Error

Example Question #102 : How To Find Circumference

A {12}'' diameter vinyl record plays music by rotating the circular disc along a fine-point needle. The attached figure shows the location of the needle in respect to the spinning record. If the needle is placed {3}'' from the outer edge of the record, what would be the "circumference" of one full rotation?
Varsity record

Possible Answers:

{18.8}''

{28.3}''

{15.7}''

{28.9}''

{25.5}''

Correct answer:

{18.8}''

Explanation:

Since the vinyl record has a diameter of {12}'' , the radius is {6}'' . If the needle is placed {3}'' from the edge of the disc, the circumference of that full rotation is calculated from a radius of {6}''-{3}'' , or a {3}'' radius. We can then find the circumference as such:

$\\circ.=\pi\cdot\2\cdot{3}''\\circ.=3.14159\cdot\2\cdot{3}''\\circ.\approx{18.8}''$

Report an Error

Example Question #103 : How To Find Circumference

If the area of a circle is $25 \pi in^2$ , what is the measure of its circumference?

Possible Answers:

$10 \pi in$

$5 \pi in$

$25 \pi in$

$50 \pi in$

Correct answer:

$10 \pi in$

Explanation:

The area of a circle is found by using the formula $area = \pi r^2$ . To figure out the radius of the circle, plug in the area given:

$25 \pi = \pi r^ 2$ divide both sides by pi

25 = r^2 take the square root of both sides

5 = r

Now we can plug that into the formula for the circumference, $C = 2 \pi r$ . Here, $C = 2 \pi \cdot 5 = 10 \pi$

Report an Error

Example Question #108 : How To Find Circumference

What is the circumference of a circle with diameter of 60cm?

Possible Answers:

$900\pi cm$

$300\pi cm$

$3600\pi cm$

$30\pi cm$

$60\pi cm$

Correct answer:

$60\pi cm$

Explanation:

The circumference formula for a circle ism

$C=2\pi r$

The Radius of the circle is half the diameter, in this case 30.

Now substitute the radius into the circumference formula to solve.

$C=2\pi30cm$

$C=60\pi cm$

Report an Error

View Tutors

Sylvanus
Certified Tutor

university of Yaounde I, Bachelor of Science, Psychology. university of Yaounde I, Master of Science, Education.

View Tutors

Jethro
Certified Tutor

Federal University of Agriculture Abeokuta,, Bachelor of Engineering, Mechatronics, Robotics, and Automation Engineering.

View Tutors

Eugenia
Certified Tutor

University of Chicago, Bachelor in Arts, Art History, Criticism, and Conservation.

All Basic Geometry Resources

9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Physics Tutors in San Diego, Statistics Tutors in Chicago, Math Tutors in New York City, SAT Tutors in Washington DC, Biology Tutors in Boston, Physics Tutors in New York City, MCAT Tutors in Philadelphia, Reading Tutors in Philadelphia, English Tutors in Phoenix, SSAT Tutors in San Diego

Popular Courses & Classes

Spanish Courses & Classes in Los Angeles, GRE Courses & Classes in Seattle, GRE Courses & Classes in Philadelphia, GMAT Courses & Classes in Washington DC, LSAT Courses & Classes in Seattle, GRE Courses & Classes in Chicago, Spanish Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in San Diego, ACT Courses & Classes in Miami, LSAT Courses & Classes in Washington DC

Popular Test Prep

ACT Test Prep in Miami, GMAT Test Prep in Boston, GRE Test Prep in Chicago, SAT Test Prep in Philadelphia, GMAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in New York City, SSAT Test Prep in Chicago, LSAT Test Prep in Philadelphia, LSAT Test Prep in Boston, GMAT Test Prep in Seattle

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

Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #91 : How To Find Circumference

Example Question #291 : Circles

Example Question #291 : Plane Geometry

Example Question #292 : Plane Geometry

Example Question #101 : How To Find Circumference

Example Question #293 : Plane Geometry

Example Question #102 : How To Find Circumference

Example Question #102 : How To Find Circumference

Example Question #103 : How To Find Circumference

Example Question #108 : How To Find Circumference

All Basic Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: