AP®︎ Calculus AB: 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 AB – Volumes with Cross Sections: Triangles and Semicircles.
Questions List
Topic 8.8
Question 1 Easy
Let be the region bounded by and the x-axis. The region is the base of a solid whose cross sections perpendicular to the x-axis are equilateral triangles with one side in .
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 AB 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: 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)).
