AP Calculus BC 8.8 Volumes with Known Cross Sections

Practise AP Calculus BC 8.8 questions by converting a base curve into semicircular cross-sectional areas and integrating them to calculate the volume of a solid.

Exam points

Derive the semicircular area from the vertical width of the curve, then evaluate its definite integral.

[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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CHA-5.B—Calculate volumes of solids with known cross sections using definite integrals—Topic 8.8 question 1