Diameter of a circular garden is 9.8 m. Find its area

Question

Accepted Answer

To find the area of a circular garden with a given diameter, we use the formula for the area of a circle:

$$ \text{Area} = \pi \times r^2 $$

where $ r $ is the radius of the circle. The radius is half of the diameter. Given that the diameter of the garden is 9.8 meters, the radius $ r $ is:

$$ r = \frac{9.8}{2} = 4.9 \text{ meters} $$

Now, substituting the radius into the area formula:

$$ \text{Area} = \pi \times (4.9)^2 $$

$$ \text{Area} = \pi \times 24.01 $$

Using the approximation $ \pi \approx 3.14159 $:

$$ \text{Area} \approx 3.14159 \times 24.01 $$

$$ \text{Area} \approx 75.46 \text{ m}^2 $$

Thus, the area of the circular garden is approximately 75.46 square meters, which corresponds to Option 1.

**Explanation for Other Options:**

- **Option 2 (80.46 m$^2$):** This option is incorrect because it overestimates the area. The calculation using the correct formula and value of $ \pi $ results in 75.46 m$^2$, not 80.46 m$^2$.

- **Option 3 (47.49 m$^2$):** This option is incorrect because it underestimates the area. The correct calculation shows that the area is significantly larger than 47.49 m$^2$.

- **Option 4 (75.86 m$^2$):** This option is incorrect because it slightly overestimates the area. The precise calculation using $ \pi \approx 3.14159 $ gives 75.46 m$^2$, not 75.86 m$^2$.

Therefore, based on the calculations and logical reasoning, Option 1 is indeed the correct answer.