A = \pi r^2 = 3.14 \times 6m \times 6m = 3.14 \times 36m^2 = 113.04 m^2
The Correct Answer and Explanation is:
Correct Calculation:
The area of a circle is given by the formula:
A=πr2A = \pi r^2
Substituting π=3.14\pi = 3.14 and r=6mr = 6m:
A=3.14×(6m×6m)A = 3.14 \times (6m \times 6m)
A=3.14×36m2A = 3.14 \times 36m^2
A=113.04m2A = 113.04m^2
Thus, the correct answer remains 113.04 square meters.
Explanation:
The formula for the area of a circle, A=πr2A = \pi r^2, is derived from the geometric properties of circles. The term π\pi represents the mathematical constant approximated as 3.14, and r2r^2 denotes the square of the radius. Squaring the radius ensures that the measurement reflects the entire circular region rather than just a linear distance.
In this case, the given radius is 6 meters. Applying the formula, we substitute the values accordingly. The first step involves squaring the radius, which means multiplying 6m6m by itself. This results in 36m236m^2. Next, multiplying 3.143.14 by 36m236m^2 yields 113.04m2113.04m^2. This final value represents the total area enclosed within the circle’s boundary.
The significance of this computation lies in practical applications such as land measurement, engineering design, and physics problems involving circular components. Understanding how to calculate the area of a circle aids in determining surface coverage for materials like flooring, painting, and pipe cross-sections. Additionally, circular area calculations play a role in optimizing space efficiency in manufacturing and architecture.
