The following diagram includes six circles with radius 4, one circle with radius 8, and one circle with radius 16. The area of the shaded region is $k\pi$. Find $k$.

[center][img]https://snag.gy/zNPBx0.jpg[/img][/center]
To solve for the shaded area, we need to find the area of the largest circle and subtract the areas of the white regions within it.

1. **Calculate the area of the largest circle:**
   The radius of the largest circle is 16. The area \( A \) of a circle is given by:
   \[
   A = \pi r^2
   \]
   Substituting \( r = 16 \):
   \[
   A = \pi (16)^2 = 256\pi
   \]

2. **Calculate the area of the white ring:**
   The white ring is formed by a circle with radius 8 and a smaller circle with radius 4 inside it.
   - The area of the larger circle (radius 8):
     \[
     A_{\text{large}} = \pi (8)^2 = 64\pi
     \]
   - The area of the smaller circle (radius 4):
     \[
     A_{\text{small}} = \pi (4)^2 = 16\pi
     \]
   - The area of the white ring is the difference between these two areas:
     \[
     A_{\text{ring}} = 64\pi - 16\pi = 48\pi
     \]

3. **Calculate the area of the five small white circles:**
   Each of the five small white circles has a radius of 4.
   - The area of one small circle:
     \[
     A_{\text{small circle}} = \pi (4)^2 = 16\pi
     \]
   - The total area of the five small circles:
     \[
     A_{\text{five small circles}} = 5 \times 16\pi = 80\pi
     \]

4. **Calculate the area of the shaded region:**
   The shaded area is the area of the largest circle minus the areas of the white regions (the white ring and the five small circles):
   \[
   A_{\text{shaded}} = 256\pi - 48\pi - 80\pi
   \]
   Simplifying:
   \[
   A_{\text{shaded}} = 256\pi - 128\pi = 128\pi
   \]

The final answer is \( \boxed{128\pi} \).