# 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

1. 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: $$\text{radius} = \frac{6}{2} = 3$$

1. 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: $$\text{Area} = \pi \times (3)^2$$

1. Calculate the area Now we compute the area: $$\text{Area} = \pi \times 9 = 9\pi$$

2. 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.
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The text passage contains a mathematical question about finding the area of a circle with a given diameter and provides a detailed answer, including the steps to solve the problem.
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Given a text passage, determine:
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# 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

1. 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: $$\text{radius} = \frac{6}{2} = 3$$

1. 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: $$\text{Area} = \pi \times (3)^2$$

1. Calculate the area Now we compute the area: $$\text{Area} = \pi \times 9 = 9\pi$$

2. 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.
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The text passage contains a mathematical question about finding the area of a circle with a given diameter and provides a detailed answer, including the steps to solve the problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER