Math Problem Statement
Solution
The problem asks you to calculate the shaded area (green) in each of the three square images where circles are placed inside squares. The circles are of equal size within each square, and the goal is to determine the area outside the circles but inside the square.
Let's break down each image:
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First image (1 circle in a square):
- The circle is inscribed inside the square, meaning its diameter equals the side length of the square.
- The area of the square is , where is the side length of the square.
- The area of the circle is , where is the radius of the circle, and .
- Shaded area = Square area - Circle area.
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Second image (4 circles in a square):
- There are 4 circles, each fitting into a quadrant of the square.
- Each circle’s diameter equals half the side length of the square, so the radius of each circle is .
- The total area of the 4 circles is , where .
- Shaded area = Square area - Total area of 4 circles.
-
Third image (16 circles in a square):
- There are 16 smaller circles, each placed inside a grid of 4x4 smaller squares.
- The diameter of each circle equals one-quarter the side length of the large square, so .
- The total area of the 16 circles is , where .
- Shaded area = Square area - Total area of 16 circles.
Would you like me to calculate the areas for these configurations or provide a more detailed step-by-step explanation?
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Math Problem Analysis
Mathematical Concepts
Geometry
Area of Circle
Area of Square
Formulas
Area of square = s^2
Area of circle = πr^2
Shaded area = Square area - Circle area
Theorems
Circle inscribed in a square
Suitable Grade Level
Grades 5-7
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