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Estimate the area of the pond below with a diameter of 6 m (NON-CALCULATOR) * (2 Points)

Ask by Potter Young. in the United Kingdom
Jan 13,2025

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The estimated area of the pond is approximately 28.26 square meters.

Solución

To estimate the area of the pond without using a calculator, we can use the formula for the area of a circle: \[ \text{Area} = \pi \times \text{radius}^2 \] Given that the diameter of the pond is 6 m, we can find the radius by dividing the diameter by 2: \[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{6}{2} = 3 \, \text{m} \] Now, we can substitute the radius into the formula for the area: \[ \text{Area} = \pi \times 3^2 = \pi \times 9 \] Since we are not using a calculator, we can approximate the value of \( \pi \) as 3.14. Therefore, the estimated area of the pond is: \[ \text{Area} \approx 3.14 \times 9 = 28.26 \, \text{m}^2 \] So, the estimated area of the pond is approximately 28.26 square meters.

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To find the area of a pond with a diameter of 6 meters, first, calculate the radius, which is half of the diameter. So, the radius is 3 meters. The formula for the area of a circle is A = πr². Using the approximation of π as 3 for easy estimation, you would compute the area as A ≈ 3 × (3)² = 3 × 9 = 27 square meters. Therefore, the estimated area of the pond is around 27 m². Now, remember that getting comfortable with approximations can help you solve problems quickly. If you're unsure about the value of π, you can always round it down to 3 for quick estimates, letting you focus on mastering the basics of area calculations. Try to visualize what an area of 27 m² actually represents—about the size of a small room or a couple of large desk spaces!

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