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AP Calculus BC Cha 5 B Calculate Volumes of Solids with Known Cross Sections Using Definite Integrals Topic 8 8 Questions

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.

Syllabus
Effective Fall 2020
Course
AP Calculus BC

Exam points

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

AP Calculus BC Cha 5 B Calculate Volumes of Solids with Known Cross Sections Using Definite Integrals Topic 8 8 Questions question 1

[Maximum number: 1]

The base of a solid is the region enclosed by the curve x416+y481=1\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?

A

356

B

732

C

249

D

712

E

425

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