a. The length of one side of the square is r².
b. The ratio of the circle to the square will be π:4.
c. The area of the square and the circle is computed below are:
Radius 3 has area of 9π
Radius 4 has area of 16π
Radius 2r has area of 2πr²
d. The thing that can be concluded about the relationship is that the area of the square is 4 times that of the circle.
<h3>How to calculate the area?</h3>
a. The radius is represented by r. Therefore, the length of the square will be:
= r × r
= r².
b. The area of the circle is πr² and the square is given as 4r². Therefore, the ratio will be:
= πr²/4r²
= π:4
c. Radius = 3
Area of circle = πr² = π × 3² = 9π
Area of square = 4r² = 4 × 3² = 36
Length of square = ✓36 = 6
Ratio = 1/4π
Radius = 4
Area of circle = πr² = π × 4² = 16π
Area of square = 4r² = 4 × 4² = 64
Length of square = ✓64 = 8
Ratio = 1/4π
Radius = 2r
Area of circle = πr² = π × 2r² = 2πr²
Area of square = 4r² = 4 × 2r² = 8r²
Length of square = ✓8r² = 2✓2r
Ratio = 1/4π
d. The relationship between the area of the circle and the square is that the area of the square is 4 times that of the circle.
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