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.

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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

  1. 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 ):

$$ r = \frac{d}{2} = \frac{4 \text{ cm}}{2} = 2 \text{ cm} $$

  1. 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 ):

$$ A = 3.14 \times (2 \text{ cm})^2 $$

  1. Calculate the area

Calculate ( (2 \text{ cm})^2 ) first:

$$ (2 \text{ cm})^2 = 4 \text{ cm}^2 $$

Now substitute back into the area equation:

$$ A = 3.14 \times 4 \text{ cm}^2 $$

  1. Final multiplication

Now multiply ( 3.14 \times 4 ):

$$ A = 12.56 \text{ cm}^2 $$

  1. 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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