What is the area of a circle with circumference $14Ï€?$

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Sun Dec 01, 2019 11:42 am

What is the area of a circle with circumference $14Ï€?$

A. $7$
B. $49$
C. $7\pi$
D. $14\pi$
E. $49\pi$

[spoiler]OA=E[/spoiler]

Source: Manhattan GMAT

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Source: Beat The GMAT — Problem Solving | Sun Dec 01, 2019 11:42 am

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by [email protected] » Sun Dec 01, 2019 1:37 pm

Hi VJesus12,

We're told that a circle has a circumference of 14Ï€. We're asked for the AREA of this circle. This question involves a couple of standard Geometry formulas, so you just have to write the formulas down and work through a couple of math steps to get the answer.

Circumference = 2(Ï€)(R) = 14Ï€
R = 7

Now that we have the radius, we just have to plug it into the Area formula:
Area = (Ï€)(R^2) = (Ï€)(7^2) = 49Ï€

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8177; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon Dec 09, 2019 5:34 pm

VJesus12 wrote:What is the area of a circle with circumference $14Ï€?$

A. $7$
B. $49$
C. $7\pi$
D. $14\pi$
E. $49\pi$

[spoiler]OA=E[/spoiler]

Source: Manhattan GMAT

Since the circumference is 14Ï€, the radius is 7, and the area is (7^2)Ï€ = 49Ï€.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Dec 12, 2019 6:26 am

VJesus12 wrote:What is the area of a circle with circumference $14Ï€?$

A. $7$
B. $49$
C. $7\pi$
D. $14\pi$
E. $49\pi$

[spoiler]OA=E[/spoiler]

Source: Manhattan GMAT

Circumference of a circle = 2Ï€r
Since we're told the circle has circumference 14Ï€, we can write: 2Ï€r = 14Ï€
Divide both sides of the equation by 2Ï€ to get: r = 7

Area of a circle = Ï€rÂ²
So the area of the given circle = Ï€(7Â²) = 49Ï€

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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