```{r, echo = FALSE, results = "hide"}
typ <- if(match_exams_call() %in% c("exams2pdf", "exams2nops")) ".pdf" else ".svg"
sup <- c("image68_1.eps")
sup <- gsub(".eps", typ, sup, fixed = TRUE)
include_supplement(sup, recursive = TRUE)
```

Question
========
A very long cylinder with the cross-sectional area of an equilateral
triangle of side length $a$ and specific weight $\gamma_r$ is submerged. 
\
![](image68_1`r typ`)

The water pressure at the bottom is $u=\gamma_w \cdot \frac{\sqrt{3}}{2} a$.
The buoyancy force per linear meter of the cylinder is 

Answerlist
----------
* $A_w = u \cdot a = \gamma_w \cdot \displaystyle \frac{a^2\sqrt{3}}{2}$
* $A_w = \gamma_w \cdot \displaystyle \frac{a^2\sqrt{3}}{4}$
* $A_w = (\gamma_r-\gamma_w) \cdot \displaystyle \frac{a^2\sqrt{3}}{4}$
* $A_w = \gamma_w \cdot a^2$
* $A_w = \gamma_w \cdot \displaystyle  a^2 \sqrt{\frac{3}{16}}$
* $A_w = \gamma_w \cdot \frac{\sqrt{3}}{2} a$
* $A_w = \gamma_w \cdot a \cdot \frac{1}{2} \left(\frac{\sqrt{3}}{2} a \right)$  

Meta-information
================
exname: Exercise 68 (groundwater)
extype: mchoice
exsolution: 0100101
exshuffle: 4
exextra[difficulty,numeric]: 1
exextra[category,character]: groundwater