Three-cylinder with height $4$ $m$ and radii of the base $5,3,1$ $m$ are going to put (in this order). Give an explicit formula for the following functions, you examine the functions on continuity and draw their graphs.
a)The cross-sectional area $F(h)$ of horizontal sections of the body obtained as Function of the height $h\in[0, 12]$.
b) The volume $V(h)$ of the body of height $h\in[0, 12]$.
I don't understand this example, I don't know how to start, if someone can help me I would be really thankful
I understand that the they are on top of each other. But still don't know how to calculate a) and b)
Is it not clear how the surface area of the cross section and the volume underneath is changing if you move the red plane from level zero to level 12?
$$F(h)= \begin{cases} \color{blue} {\pi2.5^2},&\text {if } 0\le h<4\\ \color{red}{\text{undefined }},& \text {if }h=4\\ ?,&\text {if }4<h<8\\ ?,&\text {if }h=8\\ ?,&\text {if }8< h\le 12.\\ \end{cases} $$
And similarly for the volume underneath...
$$V(h)= \begin{cases} \color{blue} {\pi2.5^2\times h},&\text {if } 0\le h\le4\\ \color{blue} {\pi2.5^2\times 4+\pi1.5^2\times (h-4)},& \text{ if }4<h\le8\\ ?,&\text {if }8< h\le 12.\\ \end{cases} $$
Graphs: