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The diameter of a circle is 6 cm . Find its area to the nearest tenth

Ask by Dawson Osborne. in the United States
Mar 14,2025

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Answer

The area of the circle is approximately 28.3 cm².

Solution

1. The diameter of the circle is \(6\) cm, so the radius \(r\) is half of the diameter: \[ r = \frac{6}{2} = 3 \text{ cm} \] 2. The area \(A\) of a circle is given by the formula: \[ A = \pi r^2 \] 3. Substitute the radius into the formula: \[ A = \pi (3)^2 = 9\pi \] 4. Using the approximation \(\pi \approx 3.1416\), calculate the area: \[ A \approx 9 \times 3.1416 = 28.2744 \text{ cm}^2 \] 5. Rounding to the nearest tenth: \[ A \approx 28.3 \text{ cm}^2 \]

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To find the area of a circle, you can use the formula A = πr², where r is the radius. Since the diameter is 6 cm, the radius (r) is half of that, which is 3 cm. Now, plugging in the values, the area (A) would be A = π(3 cm)² = 9π cm². Approximating π as 3.14, the area is about 28.3 cm² when rounded to the nearest tenth. Fun fact: The first known calculation of the area of a circle dates back to ancient Egypt, around 1650 BC, where they used a formula that approximated the value of π. Isn't it fascinating how this simple geometric shape has sparked mathematical curiosity for centuries? In real-world applications, understanding the area of a circle can be quite valuable! For instance, if you’re tiling a circular fountain, knowing the precise area helps you calculate how many tiles you’ll need. Or, if you’re planting a round flower bed, it ensures your plants have enough space to thrive!

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