To find the area of the circle, we need to determine the radius of the circle. According to the question, the radius of the circle is equal to the diagonal of a square.
- Step 1: Calculate the side of the square.
The formula for the area of a square is given by: \(A = s^2\), where \(s\) is the side of the square.
Given, the area of the square is 32 sq units.
So, \(s^2 = 32\).
Solving for \(s\), we get:
\(s = \sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}\) units. - Step 2: Calculate the diagonal of the square.
The formula for the diagonal \(d\) of a square is: \(d = s\sqrt{2}\).
Substituting the value of \(s\):
\(d = 4\sqrt{2} \times \sqrt{2} = 4 \times 2 = 8\) units.
Hence, the radius of the circle is 8 units. - Step 3: Calculate the area of the circle.
The formula for the area of a circle is: \(A = \pi r^2\), where \(r\) is the radius of the circle.
Substituting \(r = 8\) units:
\(A = \pi (8)^2 = 64\pi\) sq units.
After conducting all calculations and steps, through a proper step-by-step approach, we have found that the area of the circle is 64π square units. This answer, however, contradicts the correct answer provided (16π sq units). This suggests that there might be a possible discrepancy in the problem statement or options given. However, assuming the calculations based on the given problem, the correct computations have been provided as per the available data. Based on usual test settings, it is advisable to verify such discrepancies with further support if applicable.
Therefore, the area of the circle is \(64\pi\) sq units, assuming correct input conversions, being a part of a typical understanding and testing setup.
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Important Questions from Circles
If 3x + y - 5 = 0 is the equation of a chord of the circle x2 + y2 - 25 = 0, then what are the coordinates of the mid-point of the chord ?
What is the area of minor segment ?
What is the area of major segment ?
A straight line x = y + 2 touches the circle 4(x 2+ y 2) = r 2. The value of r is
If the centre of the circle passing through the origin is (3, 4), then the intercepts cut off by the circle on x-axis and y-axis respectively are
