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

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BTGmoderatorLU: Moderator; Posts: 2650; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Tue May 15, 2018 3:10 pm

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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. Ï€
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.

Source: Beat The GMAT — Problem Solving | Tue May 15, 2018 3:10 pm

Vincen: 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.

Jeff@TargetTestPrep: 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 16π, what is the length of an arc on the circle formed by a central angle measuring 45 degrees?

A. π
B. 3π/2
C. 2π
D. 5π/2
E. 8π

Let’s first determine the radius of the circle. Since the area is 16π:

Area = π x radius^2

16π = π x radius^2

16 = radius^2

radius = 4

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

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/8π

1/8 = x/8π

8x = 8π

x = π

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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