Find the area of a circle with diameter 18 inches.
The Correct Answer and Explanation is:
To find the area of a circle, you use the formula:A=πr2A = \pi r^2A=πr2
where AAA is the area and rrr is the radius of the circle.
The radius is half of the diameter. In this case, the diameter of the circle is 18 inches, so:r=diameter2=182=9 inchesr = \frac{diameter}{2} = \frac{18}{2} = 9 \, \text{inches}r=2diameter=218=9inches
Now, substitute the radius into the area formula:A=π(9)2A = \pi (9)^2A=π(9)2A=π×81A = \pi \times 81A=π×81A=81πA = 81\piA=81π
The value of π\piπ is approximately 3.1416. So:A≈81×3.1416=254.47 square inchesA \approx 81 \times 3.1416 = 254.47 \, \text{square inches}A≈81×3.1416=254.47square inches
Thus, the area of the circle is approximately 254.47 square inches.
Explanation:
The area of a circle depends on the square of the radius because it reflects the space within the circle. Since the radius is directly related to the diameter, we first find the radius by dividing the diameter by 2. After that, we square the radius and multiply it by π\piπ to get the area.
In practical terms, this means if you were to cover the entire surface of the circle with smaller unit squares (each 1 inch by 1 inch), you would need about 254.47 such squares to completely fill the area inside the circle.
In summary, this formula is essential in various applications such as geometry, architecture, and engineering when working with circular shapes.
