csat-suneung 2017 Q11

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

As shown in the figure, there is a solid figure with base formed by the curve $y = \sqrt { x } + 1$, the $x$-axis, the $y$-axis, and the line $x = 1$. When the cross-section of this solid figure cut by a plane perpendicular to the $x$-axis is always a square, what is the volume of this solid figure? [3 points]
(1) $\frac { 7 } { 3 }$
(2) $\frac { 5 } { 2 }$
(3) $\frac { 8 } { 3 }$
(4) $\frac { 17 } { 6 }$
(5) 3

As shown in the figure, there is a solid figure with base formed by the curve $y = \sqrt { x } + 1$, the $x$-axis, the $y$-axis, and the line $x = 1$. When the cross-section of this solid figure cut by a plane perpendicular to the $x$-axis is always a square, what is the volume of this solid figure? [3 points]\\
(1) $\frac { 7 } { 3 }$\\
(2) $\frac { 5 } { 2 }$\\
(3) $\frac { 8 } { 3 }$\\
(4) $\frac { 17 } { 6 }$\\
(5) 3

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