BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

If the area of circle O is 16Ï€, what is the length

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2544
Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members
by BTGmoderatorLU » Tue May 15, 2018 3:10 pm

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

If the area of circle O is 16Ï€, what is the length of an arc on the circle formed by a central angle measuring 45 degrees?

A. π
B. 3Ï€/2
C. 2Ï€
D. 5Ï€/2
E. 8Ï€

The OA is A.

Please, can anyone assist me with this PS question? I don't have it clear. Thanks in advance.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members
Thanked: 6 times

by Vincen » Wed May 16, 2018 12:07 am
Hello BTGmoderatorLU.

Since the area of the circle O is 16π, then we have that $$A=r^2\pi=16\pi\ \ \ \ \ \Leftrightarrow\ \ \ \ \ \ \ r^2=16\ \ \ \ \Leftrightarrow\ \ \ \ r=4.$$ Now, the length of an arc is equal to $$L=\theta\cdot r,\ \ \ where\ \theta\ is\ the\ central\ angle.$$ In our case, the central angle is 45º which is the same as π/4 and the radius is r=4.

Hence we get $$L=\theta\cdot r=\frac{\pi}{4}\cdot4=\pi.$$ Therefore, the correct answer is the option [spoiler]A. π[/spoiler].

I hope it can helps you.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members
Location: New York, NY
Thanked: 39 times

by Jeff@TargetTestPrep » Thu May 17, 2018 5:21 pm
BTGmoderatorLU wrote:If the area of circle O is 16Ï€, what is the length of an arc on the circle formed by a central angle measuring 45 degrees?

A. π
B. 3Ï€/2
C. 2Ï€
D. 5Ï€/2
E. 8Ï€
Let's first determine the radius of the circle. Since the area is 16Ï€:

Area = π x radius^2

16π = π x radius^2

16 = radius^2

radius = 4

Since circumference = 2Ï€(radius), the circumference = 2Ï€(4) = 8Ï€.

We need to determine the length of an arc on the circle formed by a central angle measuring 45 degrees. We recall that a full circle has 360 degrees.

We can create the following proportion to determine the length of the arc (which we denote as x):

45/360 = x/8Ï€

1/8 = x/8Ï€

8x = 8Ï€

x = π

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1