$\mathbf{For \space the \space first \space question:}$

We need a picture to visualize the problem.

Looking deeper at the picture, we found out that the section made by a plane running parallel through the cylinder axis and wetted diameter is a:

$$\color{blue}{\mathbf{Parabolic \space Segment}}$$

Well...it does look like an ellipse broke into two equal parts though...

$\mathbf{For \space the \space second \space question:}$

Looking deeper at the picture, we found out that the section made by a plane running perpendicular through the wetted diameter is a:

$$\color{blue}{\mathbf{Right \space Triangle}}$$

Alternate solutions are encouraged....

MATHalino

$\mathbf{For \space the \space first \space question:}$

We need a picture to visualize the problem.

Looking deeper at the picture, we found out that the section made by a plane running parallel through the cylinder axis and wetted diameter is a:

$$\color{blue}{\mathbf{Parabolic \space Segment}}$$

Well...it does look like an ellipse broke into two equal parts though...

$\mathbf{For \space the \space second \space question:}$

We need a picture to visualize the problem.

Looking deeper at the picture, we found out that the section made by a plane running perpendicular through the wetted diameter is a:

$$\color{blue}{\mathbf{Right \space Triangle}}$$

Alternate solutions are encouraged....