Armed Forces Classification Test (AFCT) Arithmetic Reasoning Practice Test

What is the area covered by a circular sprinkler if the diameter is 40ft?

1. 1,256 sq ft

2. 1,570.8 sq ft

3. 3,141.6 sq ft

4. 1,700 sq ft

The correct answer is: 1,570.8 sq ft

To find the area covered by a circular sprinkler, we use the formula for the area of a circle, which is given by: \[ \text{Area} = \pi r^2 \] where \( r \) is the radius of the circle. In this case, the diameter of the sprinkler is given as 40 feet. To find the radius, we divide the diameter by 2: \[ r = \frac{diameter}{2} = \frac{40ft}{2} = 20ft \] Now, we can substitute the radius into the area formula: \[ \text{Area} = \pi (20ft)^2 \] Calculating this, we first square the radius: \[ (20ft)^2 = 400ft^2 \] Then we multiply by \( \pi \): \[ \text{Area} = \pi \times 400ft^2 \] Using the approximate value of \( \pi \) (3.14), we can calculate the area: \[ \text{Area} \approx 3.14 \times 400ft^2 \approx 1256ft^2 \] However, for more precision, using a more accurate value for \( \