AP®︎ Calculus BC: Topic 8.8 Practice Test
Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 8.8 of AP Calculus BC – Volumes with Cross Sections: Triangles and Semicircles.
Questions List
Topic 8.8
Question 1 Easy
The base of a solid is the region bounded by , the x-axis, and . Cross sections perpendicular to the x-axis are semicircles whose diameters are the segments lying in the base region.
What is the area of the cross section at ?
What You’re Being Tested On:
Explore the learning objectives taken directly from the College Board’s AP® Calculus BC Curriculum. Ensure you’re prepared for the exact topics covered on the AP® exam, in-class tests, and quizzes, and gain confidence in your mastery of the material.
Topic 8.8: Volumes with Cross Sections: Triangles and Semicircles
Learning Objective: CHA-5.B
Calculate volumes of solids with known cross sections using definite integrals.
Essential Knowledge: CHA-5.B.2
Volumes of solids with triangular cross sections can be found using definite integrals and the area formulas for these shapes.
Essential Knowledge: CHA-5.B.3
Volumes of solids with semicircular and other geometrically defined cross sections can be found using definite integrals and the area formulas for these shapes. Illustrative examples of other cross sections in CHA-5.B.3: The volume of a funnel whose cross sections are circles can be found using the area formula for a circle and definite integrals (see 2016 AB Exam FRQ #5(b)). The volume of a solid whose cross sectional area is defined using a function can be found using the known area function and a definite integral (see 2009 AB Exam FRQ #4(c)).
