The diameter of a circle is 4 centimeters. What is the circle's area? Use π ≈ 3.14 and round your answer to the nearest hundredth.
Understand the Problem
The question is asking for the area of a circle given its diameter. We will use the formula for the area of a circle, A = πr², where r is the radius. Since the diameter is provided, we can calculate the radius by dividing the diameter by 2.
Answer
The area of the circle is \( 12.56 \text{ cm}^2 \).
Answer for screen readers
The area of the circle is ( 12.56 \text{ cm}^2 ).
Steps to Solve
- Calculate the radius from the diameter
To find the radius, divide the diameter by 2. Given that the diameter ( d = 4 ) cm, we calculate the radius ( r ):
$$ r = \frac{d}{2} = \frac{4 \text{ cm}}{2} = 2 \text{ cm} $$
- Use the area formula
Now, use the area formula for a circle, ( A = \pi r^2 ). We will substitute the radius and use ( \pi \approx 3.14 ):
$$ A = 3.14 \times (2 \text{ cm})^2 $$
- Calculate the area
Calculate ( (2 \text{ cm})^2 ) first:
$$ (2 \text{ cm})^2 = 4 \text{ cm}^2 $$
Now substitute back into the area equation:
$$ A = 3.14 \times 4 \text{ cm}^2 $$
- Final multiplication
Now multiply ( 3.14 \times 4 ):
$$ A = 12.56 \text{ cm}^2 $$
- Rounding the area
Round the result to the nearest hundredth. Since there's no extra digit beyond the hundredths:
$$ A \approx 12.56 \text{ cm}^2 $$
The area of the circle is ( 12.56 \text{ cm}^2 ).
More Information
The area of a circle is dependent on its radius, and since the diameter is a straightforward measurement, the conversion to radius is a critical first step. Always remember to use a value for ( \pi ) if instructed.
Tips
- Miscalculating the radius by forgetting to divide the diameter by 2.
- Forgetting to square the radius when calculating the area.
- Not rounding the final answer correctly.
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