AP Calculus BC 8.8 Cross-Section Volumes Overview

Build a volume integral from a base region and the area formula for each perpendicular cross section, then use bounds and geometry to justify the model.

Exam points

identify the governing calculus relationship in the problem
justify the result with symbolic, graphical or contextual evidence

Covered syllabus points

CHA-5.B—Calculate volumes of solids with known cross sections using definite integrals—Topic 8.8

[Maximum number: 1]

The base of a solid is the region enclosed by the curve $\frac{x^{4}}{16}+\frac{y^{4}}{81}=1$ shown in the figure above. For the solid, each cross section perpendicular to the x-axis is a semicircle. What is the volume of the solid?

356

732

249

712

425

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Covered syllabus points

8.8 Volumes with Cross Sections: Triangles and Semicircles question 1