{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_1r 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