We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : Circles

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find The Length Of A Chord

In the figure below, and are radii of the circle. If the radius of the circle is 8 units, how long, in units, is chord ?

Circle

Possible Answers:

$8\sqrt2$

$4\sqrt2$

$16\sqrt2$

Correct answer:

$8\sqrt2$

Explanation:

The radii and the chord form right triangle AOB . Use the Pythagorean Theorem to find the length of .

$8^2+8^2={AB}^2$

Report an Error

Example Question #1 : Circles

A circle has a maximum chord length of inches. What is its radius in inches?

Possible Answers:

Correct answer:

Explanation:

Keep in mind that the largest possible chord of a circle is its diameter.

This means that the diameter of the circle is inches, which means an -inch radius.

Remember that d = 2r ,

$\\16=2r\\ \\ \frac{16}{2}=\frac{2r}{2}\\ \\ 8=r$

Report an Error

Example Question #1 : Circles

In the circle with center A, shown below, the length of radius $\overline{AB}$ is 4 mm. What is the length of chord $\overline{BC}$ ?

Circle_chord

Possible Answers:

$2\sqrt{3}$

$4\sqrt{3}$

$8\sqrt{2}$

$2\sqrt{2}$

$4\sqrt{2}$

Correct answer:

$4\sqrt{2}$

Explanation:

In order to solve this question, we need to notice that the radii of the circle and chord $\overline{BC}$ form a right triangle with $\overline{BC}$ as the hypotenuse. We can use the Pythagorean theorem to find chord $\overline{BC}$ .

a^2 + b^2 = c^2

$4^2 + 4^2 = \overline{BC}^2$

$32 = \overline{BC}^2$

$\sqrt{32} = \overline{BC}$

$\sqrt{16\cdot 2} = \overline{BC}$

$4\sqrt{2} = \overline{BC}$

Report an Error

Example Question #1 : How To Find The Distance Between Clock Hands

A church commissioned a glassmaker to make a circular stained glass window that was two feet in diameter. What is the area of the stained glass window, to the nearest square foot?

Possible Answers:

$12\:ft^2$

$5\:ft^2$

$3\:ft^2$

$8\:ft^2$

$2\:ft^2$

Correct answer:

$3\:ft^2$

Explanation:

To answer this question, we need to find the area of a circle.

To find the area of a circle, we will use the following equation:

$area=\pi r^{2}$ , where is the radius.

We are given the diameter of the circle, which is $2\:ft$ . To find the radius of a circle, we divide the diameter by two. So, for this data:

$radius=\frac{diameter}{2}=\frac{2\:ft}{2}=1\:ft$

So, our radius is $1\:ft$ .

We can now plug our radius into our equation for the area of a circle:

$area=\pi r^{2}=\pi \cdot (1\:ft)^{2}=\pi \cdot 1\:ft^2=\pi\:ft^2=3.14\:ft^2$

The answer asks us what the area is to the nearest square foot. Therefore, we must round our answer to the nearest whole number. To round, we will round up if the digit right before your desired place value is 5, 6, 7, 8, or 9, and we will round down if it is 0, 1, 2, 3, or 4. Because we want the nearest square foot, we will look at the tenths place to aid in our rounding. Because there is a 1 in the tenths place, we will round down. So:

$3.14\:ft^2\rightarrow3\:ft^2$

Therefore, our answer is $3\:ft^2$ .

Report an Error

Example Question #1 : How To Find The Angle Of Clock Hands

What is the measure of the larger angle formed by the hands of a clock at 5:00 ?

Possible Answers:

$150^{\circ}$

$260^{\circ}$

$180^{\circ}$

$210^{\circ}$

$240^{\circ}$

Correct answer:

$210^{\circ}$

Explanation:

Like any circle, a clock contains a total of $360^{\circ}$ . Because the clock face is divided into equal parts, we can find the number of degrees between each number by doing $\frac{360}{12}=30^{\circ}$ . At 5:00 the hour hand will be at 5 and the minute hand will be at 12. Using what we just figured out, we can see that there is an angle of $150^{\circ}$ between the two hands. We are looking for the larger angle, however, so we must now do $360^{\circ}-150^{\circ}=210^{\circ}$ .

Report an Error

Example Question #1 : How To Find The Distance Between Clock Hands

Assuming the clock hands extend all the way to the edge of the clock, what is the distance between the clock hands of an analog clock with a radius of 6 inches if the time is 2:30? Reduce any fractions in your answer and leave your answer in terms of $\pi$

Possible Answers:

$\frac{17}{2}\pi$ inches

$14\pi$ inches

$7\pi$ inches

$\frac{14}{3}\pi$ inches

$\frac{7}{2}\pi$ inches

Correct answer:

$\frac{7}{2}\pi$ inches

Explanation:

To find the distance between the clock hands, first find the angle between the clock hands and use that as your central angle to find the porportion of the circumference.
The angle between the hands is $105^{\circ}$ :

$\\ \frac{105}{360} * 2*\pi*r \\ \\ \frac{105}{360}*2\pi * 6 \\ \\= \frac{7}{2}\pi inches$

Report an Error

Example Question #2 : Circles

An watch with a face radius of $35\textup{cm}$ displays the current time as $7\textup{:}20$ . Assuming each hand reaches to the edge of the clock face, what is the distance, in $\textup{cm}$ , of the minor arc between the hour and minute hand? Leave $\pi$ in your answer. Assume a $\textup{12-hour}$ display (not a military clock).

Possible Answers:

$\frac{4\pi}{17}\textup{cm}$

$\frac{130\pi}{7}\textup{cm}$

$\frac{175\pi}{9}\textup{cm}$

$\frac{15\pi}{19}\textup{cm}$

$\frac{27\pi}{7}\textup{cm}$

Correct answer:

$\frac{175\pi}{9}\textup{cm}$

Explanation:

To start, we must calculate the circumference along the clock face. Since we are required to leave $\pi$ in our answer, this is as easy as following our equation for circumference:

$C=2r\pi = 70\pi$

Next, we must figure out the positions of the hands. At $7\textup{:}20$ , the clock's minute hand would be exactly on the , and the hour hand would be $\frac{20}{60} = \frac{1}{3}$ of the way between the and the . Therefore, the total distance d(m) in terms of hour markings is $d(m) = 7\frac{1}{3} - 4 = 3\frac{1}{3}$ .

To find the distance between adjacent numbers, divide the circumference by :

$d(h) = \frac{C}{12} = \frac{70\pi}{12} = \frac{35\pi}{6}$ , where d(h) is the distance in inches between adjacent hours on the clock face.

Finally, multiply this distance by the number of hours between the hands.

$d = d(m)\cdot d(h) = 3\frac{1}{3}\cdot\frac{35\pi}{6} = \frac{10}{3}\cdot \frac{35\pi}{6} = \frac{175\pi}{9}$ .

Thus, the hands are $\frac{175\pi}{9}\textup{cm}$ apart.

Report an Error

Example Question #5 : Circles

An military ( $\textup{24-hour}$ ) clock with a face diameter of $3\textup{ft}$ displays the current time as $13\textup{:}30$ . Assuming each hand reaches to the edge of the clock face, what is the distance, in feet, of the minor arc between the hour and minute hand? Leave $\pi$ in your answer.

Possible Answers:

$\frac{5\pi}{4}\textup{ft}$

$\frac{3\pi}{16}\textup{ft}$

$\frac{5\pi}{16}\textup{ft}$

$\frac{\pi}{2}\textup{ft}$

$\frac{3\pi}{4}\textup{ft}$

Correct answer:

$\frac{3\pi}{16}\textup{ft}$

Explanation:

To start, we must calculate the circumference along the clock face. Since we are required to leave $\pi$ in our answer, this is as easy as following our equation for circumference:

$C=D\pi = 3\pi$

Next, we must figure out the positions of the hands. For this problem, the clock has 24 evenly spaced numbers instead of 12, so we must cut the distance between each number mark in half compared to a normal clock face. At 13:30 , the clock's minute hand would be exactly on the , and the hour hand would be $\frac{30}{60} = \frac{1}{2}$ of the way between the and the (remember, there are still only seconds in a minute even on a 24-hour clock. Therefore, the total distance d(m) in terms of hour markings is $d(m) = 13\frac{1}{2} -12 = 1\frac{1}{2}$ .

To find the distance between adjacent numbers, divide the circumference by :

$d(h) = \frac{C}{24} = \frac{3\pi}{24} = \frac{1\pi}{8}$ , where d(h) is the distance in feet between adjacent hours on the clock face.

Finally, multiply this distance by the number of hours between the hands.

$d = d(m)\cdot d(h) = 1\frac{1}{2}\cdot\frac{\pi}{8} = \frac{3\pi}{16}$ .

Thus, the hands are $\frac{3\pi}{16}$ feet apart.

Report an Error

Example Question #4 : How To Find The Distance Between Clock Hands

An outdoor clock with a face diameter of $18\textup{ft}$ displays the current time as $05\textup{:}45$ . Assuming each hand reaches to the edge of the clock face, what is the distance, in feet, of the minor arc between the hour and minute hand? Leave $\pi$ in your answer. Assume a $\textup{12-hour}$ display (not a military clock).

Possible Answers:

$\frac{13\pi}{3}\textup{ft}$

$4\pi\textup{ft}$

$\frac{39\pi}{8}\textup{ft}$

$\frac{3\pi}{4}\textup{ft}$

$\frac{33\pi}{2}\textup{ft}$

Correct answer:

$\frac{39\pi}{8}\textup{ft}$

Explanation:

To start, we must calculate the circumference along the clock face. Since we are required to leave $\pi$ in our answer, this is as easy as following our equation for circumference:

$C=D\pi = 18\pi$

Next, we must figure out the positions of the hands. At $05\textup{:}45$ , the clock's minute hand would be exactly on the , and the hour hand would be $\frac{45}{60} = \frac{3}{4}$ of the way between the and the . Therefore, the total distance d(m) in terms of hour markings is $d(m) = 9- 5\frac{3}{4} = 3\frac{1}{4}$ .

To find the distance between adjacent numbers, divide the circumference by :

$d(h) = \frac{C}{12} = \frac{18\pi}{12} = \frac{3\pi}{2}$ , where d(h) is the distance in inches between adjacent hours on the clock face.

Finally, multiply this distance by the number of hours between the hands.

$d = d(m)\cdot d(h) = 3\frac{1}{4}\cdot\frac{3\pi}{2} = \frac{39\pi}{8}$ .

Thus, the hands are $\frac{39\pi}{8}$ feet apart.

Report an Error

Example Question #1 : How To Find The Distance Between Clock Hands

Find the distance between the hour and minute hand of a clock at 2:00 with a hand length of .

Possible Answers:

$4\pi$

$12\pi$

$9\pi$

$2\pi$

Correct answer:

$2\pi$

Explanation:

To find the distance, first you need to find circumference. Thus,

$C=2\pi{r}=2\cdot\pi\cdot6=12\pi$

Then, multiply the fraction of the clock they cover. Thus,

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

Report an Error

View ACT Math Tutors

Ayan
Certified Tutor

Vellore Institute of Technology, Bachelor, Chemical Engineering. University of Calgary, Master's/Graduate, Chemical and Petro...

View ACT Math Tutors

Omar
Certified Tutor

Arizona State University, Bachelors, Civil Engineering.

View ACT Math Tutors

Bhupinder
Certified Tutor

Panjab University, Bachelor of Engineering, Biotechnology. Hamburg University of Technology, Master of Science, Chemical Engi...

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors

Popular Courses & Classes

SAT Courses & Classes in Philadelphia, MCAT Courses & Classes in Boston, ISEE Courses & Classes in Miami, GMAT Courses & Classes in Denver, GRE Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Boston, MCAT Courses & Classes in Chicago, GMAT Courses & Classes in Chicago, SSAT Courses & Classes in Philadelphia

Popular Test Prep

SSAT Test Prep in Boston, GRE Test Prep in Houston, SAT Test Prep in San Diego, LSAT Test Prep in San Diego, SSAT Test Prep in Denver, SAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Dallas Fort Worth, GRE Test Prep in Dallas Fort Worth, ISEE Test Prep in Seattle, ACT Test Prep in Boston

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

ACT Math : Circles

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Find The Length Of A Chord

Example Question #1 : Circles

Example Question #1 : Circles

Example Question #1 : How To Find The Distance Between Clock Hands

Example Question #1 : How To Find The Angle Of Clock Hands

Example Question #1 : How To Find The Distance Between Clock Hands

Example Question #2 : Circles

Example Question #5 : Circles

Example Question #4 : How To Find The Distance Between Clock Hands

Example Question #1 : How To Find The Distance Between Clock Hands

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: