The circumference of a circular stained glass window is 18\pi inches. What is the area of … — Armed Services Vocational Aptitude Battery (ASVAB)

The circumference of a circular stained glass window is $18\pi$ inches. What is the area of the window in square inches?

(Enter only the numerical value that multiplies $\pi$ . For example, if the area is $10\pi$ , enter 10.)

Cevap: 81

The correct answer is 81. First, the radius is found by dividing the circumference (

18\pi

) by

2\pi

, which gives a radius of 9 inches. Then, the area is calculated by squaring this radius and multiplying by

\pi

(

9^2 = 81

), resulting in a total area of

81\pi

. Since the prompt asks for just the numerical value multiplying

\pi

, the final response is 81.

Find the radius of the circular window using the circumference formula

C = 2\pi r

18\pi = 2\pi r \Rightarrow r = 9

inches.

The area formula requires the radius, so we must work backward from the given circumference to find it.

Calculate the area of the window using the area formula

A = \pi r^2

A = \pi(9)^2 = 81\pi

square inches.

Squaring the radius and multiplying by

\pi

yields the total area of the circle.

Identify the requested numerical value.

The question specifically asks for the numerical coefficient that multiplies

\pi

Calculating the area of a circle by first determining the radius from the circumference.

Soru