A circular security zone has a circumference of 16\pi meters. What is the area of this zon… — Armed Services Vocational Aptitude Battery (ASVAB)

A circular security zone has a circumference of $16\pi$ meters. What is the area of this zone in square meters?

64\pi

To find the area, the radius of the circle must first be determined using the circumference formula (

C = 2\pi r

). Setting the given circumference equal to the formula (

16\pi = 2\pi r

) gives a radius of

8

meters. The area is then calculated using the formula

A = \pi r^2

, which results in

\pi(8)^2 = 64\pi

square meters.

Identify the formula for circumference to solve for the radius.

C = 2\pi r = 16\pi

The radius is required to calculate the area of the circle.

Solve for the radius (

r

r = 8

meters

Dividing both sides of the equation by

2\pi

isolates the radius.

Apply the area formula for a circle using the found radius.

A = \pi r^2 = \pi(8)^2 = 64\pi

square meters

Substituting the radius (

8

) into the area formula yields the final required value.

Calculating the area of a circle by first deriving its radius from a given circumference.

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