AP Calculus BC Cha 5 C Calculate Volumes of Solids of Revolution Using Definite Integrals Topic 8 11 Questions

Practise AP Calculus BC 8.11 by choosing inner and outer radii, setting bounds in the correct variable, and evaluating washer-method volume integrals.

Exam points

Set up π∫(R²−r²) using the correct inner and outer radii for rotation about an axis.
Choose x- or y-integration bounds so the washer slices stay perpendicular to the rotation axis.

[Maximum number: 1]

Let R be the region in the first quadrant bounded by the graph of $y=\sqrt{x-1}$ , the x-axis, and the vertical line x=10. Which of the following integrals gives the volume of the solid generated by revolving R about the y-axis?

$\pi \int_{1}^{10}(x-1) d x$

$\pi \int_{1}^{10}(100-(x-1)) d x$

$\pi \int_{0}^{3}\left(10-\left(y^{2}+1\right)\right)^{2} d y$

$\pi \int_{0}^{3}\left(100-\left(y^{2}+1\right)^{2}\right) d y$

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AP Calculus BC Cha 5 C Calculate Volumes of Solids of Revolution Using Definite Integrals Topic 8 11 Questions question 1