Step 1: Understand the arrangement
The six smaller circles form a ring with one smaller circle in the center. This is a common packing pattern.

Step 2: Define variables
Let the radius of each smaller circle be $r$.
Their area is:

$$
\(A_{\text {small }}=\pi r^2\)
$$


Step 3: Larger circle radius and arrangement
- The center small circle has radius $r$.
- The six outer small circles are arranged around this center circle, and each touches it and its two neighboring small circles.

The centers of the outer six small circles form a regular hexagon around the center circle's center.
The distance from the center circle's center to each outer circle's center is $2 r$ because each small circle touches the center circle.

Hence, the radius of the larger circle must cover the outer circle radius plus $r$ (the radius of the outer small circle).

So the radius $R$ of the larger circle is:

$$
\(R=3 r\)
$$

Step 4: Areas of the circles
- Area of one smaller circle:

$$
\(\pi r^2\)
$$

- Total area of the 7 smaller circles:

$$
\(7 \pi r^2\)
$$

- Area of the larger circle:

$$
\(\pi R^2=\pi(3 r)^2=9 \pi r^2\)
$$


Step 5: Calculate unshaded area and percent
- Unshaded area in the larger circle:

$$
\(9 \pi r^2-7 \pi r^2=2 \pi r^2\)
$$

- Percent unshaded relative to larger circle:

$$
\(\frac{2 \pi r^2}{9 \pi r^2} \times 100=\frac{2}{9} \times 100=22.22\) %
$$


Answer:
$22.22 %$ of the larger circle is unshaded.