i havent learned about cpf's yet. i i cant figure our how to find the pdf of the area and circumference. that is where i am getting stuck.

thanks for you help!

The cdf of A is given by:

\(\displaystyle G(a) = \Pr(A < a) = \Pr(\pi X^2 < a) = \Pr\left( - \frac{\sqrt{a}}{\sqrt{\pi}} < X < \frac{\sqrt{a}}{\sqrt{\pi}}\right) = \int_{0}^{\frac{\sqrt{a}}{\sqrt{\pi}}} f(x) \, dx = ....\)

for \(\displaystyle 0 < a < 4 \pi\)

and so the pdf of A is given by \(\displaystyle g(a) = \frac{dG}{da} = .... \)

The details are left for you. The pdf of C can be found in a similar way.