Call Now to Set Up Tutoring:

(888) 888-0446

Basic Geometry : Basic 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 #31 : Basic Geometry

The diameter of a circle is 16 centimeters. What is the area of the circle in centimeters?

Possible Answers:

200.96

50.24

256

803.84

Correct answer:

200.96

Explanation:

The area of a circle is found by squaring the circle's radius and multiplying the result by 3.14. The radius is half of the diameter (8 in this case).

$8^{2}\cdot 3.14=64\cdot 3.14=200.96$

Report an Error

Example Question #42 : Radius

A circle is inscribed in a square whose side is 6 in. What is the difference in area between the square and the circle, rounded to the nearest square inch?

Possible Answers:

$11\ in^{2}$

$8\ in^{2}$

$4\ in^{2}$

$12\ in^{2}$

$14\ in^{2}$

Correct answer:

$8\ in^{2}$

Explanation:

The circle is inscribed in a square when it is drawn within the square so as to touch in as many places as possible. This means that the side of the square is the same as the diameter of the circle.

Let $\pi =3.14$

$A_{square}= s^{2} = (6)^{2} = 36 in^{2}$

$A_{circle}= \pi r^{2}=3.14\cdot3^{2}=3.14\cdot9=28.26 in^{2}$

So the approximate difference is in area $8\ \textup{in}^{2}$

Report an Error

Example Question #231 : High School Math

Two equal circles are cut out of a rectangular sheet of paper with the dimensions 10 by 20. The circles were made to have the greatest possible diameter. What is the approximate area of the paper after the two circles have been cut out?

Figure_2

Possible Answers:

Correct answer:

Explanation:

The length of 20 represents the diameters of both circles. Each circle has a diameter of 10 and since radius is half of the diameter, each circle has a radius of 5. The area of a circle is A = πr² . The area of one circle is 25π. The area of both circles is 50π. The area of the rectangle is (10)(20) = 200. 200 - 50π gives you the area of the paper after the two circles have been cut out. π is about 3.14, so 200 – 50(3.14) = 43.

Report an Error

Example Question #232 : High School Math

Screen_shot_2013-03-18_at_10.29.01_pm

Kate has a ring-shaped lawn which has an inner radius of 10 feet and an outer radius 25 feet. What is the area of her lawn?

Possible Answers:

525π ft²

275π ft²

125π ft²

175π ft²

325π ft²

Correct answer:

525π ft²

Explanation:

The area of an annulus is

$\pi (R^{2}-r^{2})$

where is the radius of the larger circle, and is the radius of the smaller circle.

$\pi (25^{2}-10^{2})$

$\pi (625-100)$

$525\pi$

Report an Error

Example Question #233 : High School Math

A 6 by 8 rectangle is inscribed in a circle. What is the area of the circle?

Possible Answers:

$25\pi$

$10\pi$

$4\pi$

$20\pi$

Correct answer:

$25\pi$

Explanation:

The image below shows the rectangle inscribed in the circle. Dividing the rectangle into two triangles allows us to find the diameter of the circle, which is equal to the length of the line we drew. Using a²+b²= c² we get 6²+ 8² = c². c² = 100, so c = 10. The area of a circle is $A=\pi r^2$ . Radius is half of the diameter of the circle (which we know is 10), so r = 5.

$A=\pi *5^2=25\pi$

Diagram_1

Report an Error

Example Question #32 : Basic Geometry

What is the ratio of the area of a circle to the area of the square it circumscribes?

Possible Answers:

$\pi ^{2}\ to\ 1$

$\pi \ to\ 2$

$2\pi \ to\ 1$

$\pi \ to\ 1$

$4\ to\ \pi$

Correct answer:

$\pi \ to\ 2$

Explanation:

Since each angle of a square is a right angle, each intercepts a semicircle; as a result, a diagonal of the square doubles as a diameter of the circle. We will call that common measure d=2r , as it will make our ratio easier to calculate.

The area of the circle is $\pi r^{2}$ .

The area of the square is $\frac{1}{2} d^{2} = \frac{1}{2} (2r)^{2} = 2r^{2}$ . This formula is important, even though it is not the more commonly known formula of Area = side².

Therefore the ratio of the area of the circle to that of the square is $\pi r^{2}$ to $2 r^{2}$ , which simplifies to $\pi$ to 2.

Report an Error

Example Question #33 : Basic Geometry

What is the area of a circle with a circumference of 12 inches?

Possible Answers:

$\frac{36}{\pi }\ in^{2}$

$6\pi \ in^{2}$

$\sqrt{6\pi }\ in^{2}$

$36\pi \ in^{2}$

$\frac{6}{\pi }\ in^{2}$

Correct answer:

$\frac{36}{\pi }\ in^{2}$

Explanation:

The relationship of a circumference of a circle to its radius is $C = 2\pi r$ .

Equivalently, $r = \frac{C}{2 \pi }$ .

Set C=12 :

$r = \frac{12}{2 \pi }$

$r = \frac{6}{ \pi }$

To find the area, use the formula $A = \pi r^{2}$ .

Plug in our new value of r:

$A = \pi\left ( \frac{6}{\pi } \right ) ^{2}$

$A = \frac{36}{\pi }$ square inches

Report an Error

Example Question #234 : High School Math

A park wants to build a circular fountain with a walkway around it. The fountain will have a radius of 40 feet, and the walkway is to be 4 feet wide. If the walkway is to be poured at a depth of 1.5 feet, how many cubic feet of concrete must be mixed to make the walkway?

Possible Answers:

None of the other answers are correct.

$504\pi \ ft^{3}$

$1296\pi \ ft^{3}$

$1936\pi \ ft^{3}$

$336\pi \ ft^{3}$

Correct answer:

$504\pi \ ft^{3}$

Explanation:

The following diagram will help to explain the solution:

Foutain

We are searching for the surface area of the shaded region. We can multiply this by the depth (1.5 feet) to find the total volume of this area.

The radius of the outer circle is 44 feet. Therefore its area is 44²π = 1936π. The area of the inner circle is 40²π = 1600π. Therefore the area of the shaded area is 1936π – 1600π = 336π. The volume is 1.5 times this, or 504π.

Report an Error

Example Question #1 : Area Of A Circle

How many times greater is the area of a circle with a radius of 4in., compared to a circle with a radius of 2in.?

Possible Answers:

$2\pi$

$4\pi$

$\pi$

$2$

$4$

Correct answer:

$4$

Explanation:

The area of a circle can be solved using the equation $A=\pi r^{2}$

The area of a circle with radius 4 is $\pi 4^{2}=16\pi$ while the area of a circle with radius 2 is $\pi 2^{2}=4\pi$ . $16\pi \div 4\pi =4$

Report an Error

Example Question #235 : High School Math

What is the area of a circle whose diameter is 8?

Possible Answers:

16π

8π

12π

64π

32π

Correct answer:

16π

Explanation:

Circarea

Report an Error

View Tutors

Ria
Certified Tutor

Oregon State University, Bachelor in Arts, English.

View Tutors

Emmanuel
Certified Tutor

Baylor University, Bachelor of Science, Biology, General.

View Tutors

Victor
Certified Tutor

University of Baltimore, Bachelor, Law. University of Maryland-University College, Master of Arts, Management Science.

All Basic Geometry Resources

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

Popular Subjects

Calculus Tutors in Boston, SSAT Tutors in Houston, Chemistry Tutors in Seattle, SSAT Tutors in Washington DC, LSAT Tutors in Seattle, ACT Tutors in New York City, ACT Tutors in Miami, English Tutors in Washington DC, Spanish Tutors in Los Angeles, Statistics Tutors in Boston

Popular Courses & Classes

LSAT Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Atlanta, ISEE Courses & Classes in Boston, ACT Courses & Classes in Washington DC, GRE Courses & Classes in Houston, SSAT Courses & Classes in Houston, GMAT Courses & Classes in Boston, LSAT Courses & Classes in Phoenix, LSAT Courses & Classes in Seattle

Popular Test Prep

GMAT Test Prep in Chicago, LSAT Test Prep in Atlanta, SAT Test Prep in San Diego, ACT Test Prep in Washington DC, GMAT Test Prep in Seattle, MCAT Test Prep in San Diego, MCAT Test Prep in Seattle, ISEE Test Prep in Denver, GMAT Test Prep in Boston, ACT Test Prep in Denver

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 : Basic Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #31 : Basic Geometry

Example Question #42 : Radius

Example Question #231 : High School Math

Example Question #232 : High School Math

Example Question #233 : High School Math

Example Question #32 : Basic Geometry

Example Question #33 : Basic Geometry

Example Question #234 : High School Math

Example Question #1 : Area Of A Circle

Example Question #235 : High School Math

All Basic Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: