im trying to wrap my brain around a question ive been given by a friend. Given the distribution $f(0)^2 \cdot e^\frac{-r^2}{2\sigma^2}$, the goal is to calculate the volume between the function and the x-y Plane. The way this is supposed to be done is to use concentric cylinders - which brings me to my question. The problem states: Show that the volume of such a cylinder is given by $V(r) = f(0)^2 \cdot e^\frac{-r^2}{2\sigma^2}\cdot 2\pi\cdot r \cdot \Delta r$ It then continues on to show that the entire volume can be calculated using the following integral: $\int_0^{\infty} f(0)^2 \cdot e^\frac{-r^2}{2\sigma^2}\cdot 2\pi\cdot r dr$
I can do the integral and i understand the idea behind it. What i dont understand is the way the initial formula is set up. This whole task is done to derive some version of the normal distribution, which i have never seen to have an $f(0)$ inside of the formula.
TL;DR: whats happening with $V(r)$? why does this work to approximate said volume?
Thanks alot