A circular garden has a radius of 18 m. A 2.5 m wide pathway is constructed around it. What is the approximate area of the pathway?

`. Let's write the response cleanly. **Clean Answer:** 302 m² **Solution:** ```html

The correct option is 302 m².

To find the area of the pathway around the circular garden, we need to calculate the difference between the total area including the pathway (outer circle) and the area of the garden itself (inner circle).

Step 1: Identify the given dimensions.
Inner radius of the garden (r) = 18 m
Width of the pathway (w) = 2.5 m

Step 2: Find the outer radius (R).
The outer radius is the sum of the inner radius and the width of the pathway:

$R=r+w=18+2.5=20.5\text{ m}$

Step 3: Calculate the area of the pathway.
The formula for the area of a circular pathway (ring) is:

$\text{Area of pathway}=\pi \times (R^2-r^2)$

Substituting the values of R and r into the formula:

$\text{Area of pathway}=\pi \times ({20.5}^2-{18}^2)$

$\text{Area of pathway}=\pi \times (420.25-324)$

$\text{Area of pathway}=96.25\times \pi$

Step 4: Compute the numerical value.
Using the approximation $\pi \approx 3.1416$:

$\text{Area of pathway}=96.25\times 3.1416=302.379{\text{ m}}^2$

Rounding off to the nearest whole number gives approximately 302 m².

``` Let's double-check symbol rules: - "VERY IMPORTANT: Do NOT use HTML hex or decimal entities (like − or −) for symbols like minus or arrows. Use standard raw unicode characters like -, +, =, ⇒ directly." - Let's use raw characters directly (e.g., `-`, `+`, `=`, `×`, `π`, `≈`) without any HTML entities like `π` or `×` to be completely safe against entity parsing issues. Let's construct the output. 302 m²

The correct option is 302 m².

To find the area of the pathway around the circular garden, we calculate the difference between the area of the outer circle (which includes both the garden and pathway) and the area of the inner circle (the garden itself).

Step 1: Determine the inner and outer radii.
Inner radius of the garden (r) = 18 m
Width of the pathway (w) = 2.5 m

The outer radius (R) is the sum of the inner radius and the pathway width:

$R=r+w=18+2.5=20.5\text{m}$

Step 2: Calculate the area of the pathway.
The area of the pathway is given by the area between two concentric circles:

$\text{Area of pathway}=\pi \times (R^2-r^2)$

Substituting the values of R and r:

$\text{Area of pathway}=\pi \times ({20.5}^2-{18}^2)$

$\text{Area of pathway}=\pi \times (420.25-324)$

$\text{Area of pathway}=96.25\times \pi$

Step 3: Approximate the final value.
Using $\pi \approx 3.1416$:

$\text{Area of pathway}\approx 96.25\times 3.1416=302.379{\text{m}}^2$

Rounding to the nearest integer gives approximately 302 m².