$6$ circles of radius $4$ , one circle of radius $8$ , and one circle of radius $16$ . The shaded area is $k\pi$ . What is the value of $k = ?$

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125
128
200
225
135

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Area of the large gray circle: $16^2\pi = 256 \pi$ .

Area of the small white $5$ circles = $5\times (16\pi)= 80\pi$ and area of one gray small circle is $16\pi$ .

Area of medium white circle = $8^2\pi= 64\pi \implies$

Area of the gray shaded region = $(256 - 80 - 64+ 16)\pi = 128\pi \implies k=\boxed{128}$ .