What is the area of a circle with circumference \(14Ï€?\)

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

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

VJesus12 wrote:What is the area of a circle with circumference \(14π?\)

A. \(7\)
B. \(49\)
C. \(7\pi\)
D. \(14\pi\)
E. \(49\pi\)

[spoiler]OA=E[/spoiler]

Source: Manhattan GMAT

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

Area of a circle = πr²
So the area of the given circle = π(7²) = 49π

Answer: E

Cheers,
Brent