A garden is circular with a border 3 m wide around it. The total area including border is 794 m², and the garden area alone is 379.94 m². What is the radius of the garden?

The correct answer is 11 m.

Step 1: Understand the given data
Let the radius of the circular garden be $r$ meters.
The border around the garden has a width of 3 m.
Therefore, the outer radius including the border is $R=r+3$ meters.
We are given that the area of the garden alone is 379.94 m².

Step 2: Formula for the area of a circle
The area of a circle is given by the formula:

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

Step 3: Calculate the radius of the garden
Using the area of the garden alone:

$\pi r^2=379.94$

Using $\pi \approx 3.14$:

$3.14\times r^2=379.94$

Divide both sides by 3.14:

$r^2=\frac{379.94}{3.14}$

$r^2=121$

Taking the square root on both sides:

$r=\sqrt{121}=11\text{ m}$

Thus, the radius of the garden is 11 m.