The area of a circle is calculated using the formula A equals pi times r squared. Here, A represents the area, π (pi) is approximately 3.14159, and r is the radius of the circle.
The radius of a circle is the distance from the center point to any point on the circle's edge. In our problem, we are given that the radius is 7 centimeters.
Now we substitute the given radius value into the formula. Starting with A equals pi r squared, we replace r with 7, giving us A equals pi times 7 squared. This simplifies to A equals pi times 49.
To find the area, we calculate pi times 49. The exact answer is 49 pi square centimeters. For a decimal approximation, we multiply 49 by 3.14159, which gives us approximately 153.94 square centimeters.
Here is our final solution visualized. We started with a circle of radius 7 centimeters. Using the formula A equals pi r squared, we calculated the area to be exactly 49 pi square centimeters, or approximately 153.94 square centimeters. This visualization confirms our mathematical result.