csat-suneung 2020 Q12

csat-suneung · South-Korea · csat__math-science 3 marks Volumes of Revolution Volume by Cross Sections with Known Geometry

As shown in the figure, for a positive number $k$, the region enclosed by the curve $y = \sqrt { \frac { e ^ { x } } { e ^ { x } + 1 } }$, the $x$-axis, the $y$-axis, and the line $x = k$ is the base of a solid figure. When the cross-section perpendicular to the $x$-axis is always a square and the volume is $\ln 7$, what is the value of $k$? [3 points]
(1) $\ln 11$
(2) $\ln 13$
(3) $\ln 15$
(4) $\ln 17$
(5) $\ln 19$

As shown in the figure, for a positive number $k$, the region enclosed by the curve $y = \sqrt { \frac { e ^ { x } } { e ^ { x } + 1 } }$, the $x$-axis, the $y$-axis, and the line $x = k$ is the base of a solid figure. When the cross-section perpendicular to the $x$-axis is always a square and the volume is $\ln 7$, what is the value of $k$? [3 points]\\
(1) $\ln 11$\\
(2) $\ln 13$\\
(3) $\ln 15$\\
(4) $\ln 17$\\
(5) $\ln 19$

Paper Questions

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