AHSME 1968 Problem 1

Let $P$ units be the increase in circumference of a circle resulting from an increase in $\pi$ units in the diameter. Then $P$ equals: $\text{(A) } \frac{1}{\pi} \text{(B) } \pi \text{(C) } \frac{\pi^2}{2} \text{(D) } \pi^2 \text{(E) } 2\pi$