Calculate the area of a circle with a radius of 3

Solution By Steps

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

$$A=\pi r^2$$

where $r$ is the radius of the circle.

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

$$A=\pi (3{)}^2$$

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

$$A=\pi \times 9$$

Then multiply by $\pi$:

$$A=9\pi$$

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

$$A\approx 9\times 3.1416=28.2744$$

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

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

Key Concept Explanation
The formula $A=\pi r^2$ 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 $\pi$ (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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