Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Four circles, each with a radius of 2 inches, are removed from a square. What is the remaining area of the square?

A. [tex]\( (16-4\pi) \)[/tex] in.[tex]\(^2\)[/tex]
B. [tex]\( (16-\pi) \)[/tex] in.[tex]\(^2\)[/tex]
C. [tex]\( (64-16\pi) \)[/tex] in.[tex]\(^2\)[/tex]
D. [tex]\( (64-4\pi) \)[/tex] in.[tex]\(^2\)[/tex]

Sagot :

GinnyAnswer
Let's solve the problem step by step to find the remaining area of the square after removing four circles, each with a radius of 2 inches.

### Step 1: Calculate the Area of One Circle
The radius of each circle is given as 2 inches. The formula to find the area of a circle is:
[tex]\[ \text{Area of a Circle} = \pi \times \text{radius}^2 \][/tex]

Substituting the radius:
[tex]\[ \text{Area of one circle} = \pi \times 2^2 = 4\pi \text{ square inches} \][/tex]

### Step 2: Calculate the Total Area of the Four Circles
Since there are four circles, we multiply the area of one circle by 4:
[tex]\[ \text{Total Area of Four Circles} = 4 \times 4\pi = 16\pi \text{ square inches} \][/tex]

### Step 3: Calculate the Side Length of the Square
Each radius of the circle is 2 inches. Since we are given that four circles are removed from the square, it implies the side length of the square is the diameter of one circle multiplied by 2 (because we need to fit two circles side by side along one side of the square). The diameter of one circle is:
[tex]\[ \text{Diameter} = 2 \times \text{Radius} = 2 \times 2 = 4 \text{ inches} \][/tex]

Therefore, the side length of the square is the same as the diameter of one circle since four circles make a cross pattern in the square with length:
[tex]\[ \text{Side Length of the Square} = 2 \times \text{Diameter} = 2 \times 2 \times 2 = 4 \text{ inches} \][/tex]

### Step 4: Calculate the Area of the Square
To find the area of the square, use the side length:
[tex]\[ \text{Area of the Square} = \text{Side Length}^2 = 4^2 = 16 \text{ square inches} \][/tex]

### Step 5: Calculate the Remaining Area
The remaining area of the square after removing the area occupied by the four circles is:
[tex]\[ \text{Remaining Area} = \text{Area of the Square} - \text{Total Area of Four Circles} \][/tex]

Substitute the values:
[tex]\[ \text{Remaining Area} = 16 - 16\pi \text{ square inches} \][/tex]

So, the final solution provided by this is:
[tex]\[ \boxed{16 - 16\pi \text{ square inches}} \][/tex]

Hence, the correct answer is:
[tex]\[ (16 - 16\pi) \text{ square inches} \][/tex]
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.