Calculate the area of a circle with a radius of 3

1 min read

Solution By Steps

Step 1: Recall the formula for the area of a circle
The area AA of a circle is given by the formula:

A=πr2A = \pi r^2

where rr is the radius of the circle.

Step 2: Substitute the radius value into the formula
Given that the radius r=3r = 3, substitute this value into the formula:

A=π(3)2A = \pi (3)^2

Step 3: Simplify the expression
First, square the radius:

A=π×9A = \pi \times 9

Then multiply by π\pi:

A=9πA = 9\pi

Step 4: Approximate the result
Using the approximation π≈3.1416\pi \approx 3.1416:

A≈9×3.1416=28.2744A \approx 9 \times 3.1416 = 28.2744

Final Answer
The area of the circle is 9π9\pi or approximately 28.27 square units28.27 \, \text{square units}.


Key Concept
The area of a circle depends on the square of the radius and is directly proportional to π\pi, a constant that relates the circumference and diameter of any circle.

Key Concept Explanation
The formula A=πr2A = \pi r^2 tells us that the area of a circle increases with the square of its radius. This means that if the radius doubles, the area increases by a factor of four. The constant π\pi (approximately 3.1416) is essential in calculating areas and circumferences of circles, as it represents the ratio of the circumference of any circle to its diameter.


Related Knowledge or Questions
[1] What is the circumference of a circle with the same radius?
[2] How does the area change if the radius is doubled?
[3] Derive the area formula for a circle from the circumference formula.

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