The circular foundation of a radar dome has a circumference of 36\pi \text{ feet}. What is… — Armed Services Vocational Aptitude Battery (ASVAB)

The circular foundation of a radar dome has a circumference of $36\pi \text{ feet}$ . What is the area of this circular foundation, in square feet?

(Enter only the numerical coefficient of $\pi$ in your answer. For example, if the area is $100\pi$ , enter 100.)

Answer: 324

324

The circumference of a circle is calculated using

C = 2\pi r

. Setting the given circumference

36\pi = 2\pi r

gives a radius of

18 \text{ feet}

. The area is found using

A = \pi r^2

, which becomes

A = \pi(18)^2 = 324\pi \text{ square feet}

. Since the question asks for the numerical coefficient of

\pi

, the correct value to enter is 324.

Find the radius of the circular foundation from its given circumference.

r = 18

The circumference formula is

C = 2\pi r

. Setting

2\pi r = 36\pi

allows us to solve for the radius.

Calculate the area of the foundation using the radius.

A = 324\pi

The area formula is

A = \pi r^2

. Substituting

r = 18

gives

A = \pi(18)^2 = 324\pi

Extract the numerical coefficient of

\pi

for the final answer.

324

The question explicitly asks to enter only the numerical coefficient of

\pi

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

Question