Armed Forces Classification Test (AFCT) Arithmetic Reasoning Practice Test

What area does a sprinkler cover if it sprays water in a circular region with a radius of 20 ft?

1. 200π ft²

2. 300π ft²

3. 400π ft²

4. 500π ft²

The correct answer is: 400π ft²

To find the area covered by the sprinkler, which sprays water in a circular region, we can use the formula for the area of a circle. The area \( A \) of a circle is given by the formula: \[ A = πr^2 \] where \( r \) is the radius of the circle. In this case, the radius of the sprinkler's spray area is 20 feet. Plugging this value into the formula, we will calculate the area as follows: \[ A = π(20)^2 \] Calculating \( (20)^2 \): \[ (20)^2 = 400 \] Now, substituting this back into the area formula: \[ A = 400π \] Thus, the area covered by the sprinkler is: \[ 400π \, \text{ft}^2 \] The choice that reflects this calculation is the option that states 400π ft², confirming that this is indeed the correct answer. This reasoning combines the understanding of basic geometry (specifically, the formula for the area of a circle) with straightforward arithmetic.