ap-calculus-ab 2008 Q1

ap-calculus-ab · USA · free-response_formB Volumes of Revolution Multi-Part Free Response with Area, Volume, and Additional Calculus

Let $R$ be the region in the first quadrant bounded by the graphs of $y = \sqrt { x }$ and $y = \frac { x } { 3 }$. (a) Find the area of $R$. (b) Find the volume of the solid generated when $R$ is rotated about the vertical line $x = - 1$. (c) The region $R$ is the base of a solid. For this solid, the cross sections perpendicular to the $y$-axis are squares. Find the volume of this solid.

: \text { limits }

Let $R$ be the region in the first quadrant bounded by the graphs of $y = \sqrt { x }$ and $y = \frac { x } { 3 }$.
(a) Find the area of $R$.
(b) Find the volume of the solid generated when $R$ is rotated about the vertical line $x = - 1$.
(c) The region $R$ is the base of a solid. For this solid, the cross sections perpendicular to the $y$-axis are squares. Find the volume of this solid.

Paper Questions

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