Question

A square grassy field is watered by 4 sprinklers. The sprinklers spray water in a circular pattern, as shown above. If the field has side lengths of 60 ft, what is the area of the portion of the field that will not be watered by the sprinklers?

Answer 1

The answer is (3600 - 900π) ft²

Step 1. Find the radius r of circles.
Step 2. Find the area of the portion of the field that will be watered by the sprinklers (A1)
Step 3. Find the total area of the field (A2)
Step 4. Find the area of the portion of the field that will not be watered by the sprinklers (A)

Step 1. Find the radius r of circles
r = ?
According to the image, radius of a square is one fourth of the field side length:
r = s/4
s = 60 ft
r = 60/4 = 15 ft

Step 2. Find the area of the portion of the field that will be watered by the sprinklers.
The area of the field that will be watered by the sprinklers (A1) is actually total area of 4 circles with radius 15 ft.
Since the area of a circle is π r², then A1 is:
A1 = 4 * π r² = 4 * π * 15² = 900π ft²

Step 3. Find the total area of the field (A2)
The field is actually a square with side s = 60 ft.
A2 = s² = 60² = 3600 ft²

Step 4. Find the area of the portion of the field that will not be watered by the sprinklers (A).
To get the area of the portion of the field that will not be watered by the sprinklers (A) we need to subtract the area of 4 circles from the total area:
A = A2 - A1
A = (3600 - 900π) ft²

Answer 2

I think its the 4th one