Area of a circle with a diameter of 6
Understand the Problem
The question is asking for the area of a circle given that its diameter is 6. To find the area, we will use the formula: Area = π * (radius)^2. Since the radius is half of the diameter, we will first calculate the radius (which is 3) and then use it to find the area.
Answer
The area of the circle is $9\pi$ or approximately $28.26$.
Answer for screen readers
The area of the circle is $9\pi$ or approximately $28.26$.
Steps to Solve
- Calculate the radius Since the diameter is given as 6, we can find the radius by dividing the diameter by 2. The formula is: $$ \text{radius} = \frac{\text{diameter}}{2} $$
Substituting the given diameter: $$ \text{radius} = \frac{6}{2} = 3 $$
- Use the area formula Now that we have the radius, we can find the area of the circle using the area formula: $$ \text{Area} = \pi \times (\text{radius})^2 $$
Substituting the radius we calculated: $$ \text{Area} = \pi \times (3)^2 $$
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Calculate the area Now we compute the area: $$ \text{Area} = \pi \times 9 = 9\pi $$
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Approximate the area If needed, we can approximate the area using $ \pi \approx 3.14 $: $$ \text{Area} \approx 9 \times 3.14 = 28.26 $$
The area of the circle is $9\pi$ or approximately $28.26$.
More Information
The area of a circle increases with the square of the radius. This means that even a small increase in the radius will result in a significantly larger area. For instance, if the radius were to increase from 3 to 4, the area would increase from $9\pi$ to $16\pi$.
Tips
- Forgetting to divide the diameter by 2 to find the radius.
- Misapplying the area formula by using diameter instead of radius.
- Inaccurate approximation of $\pi$ could lead to wrong answers when rounding.
