AP®︎ Calculus AB: Topic 8.7 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 8.7 of AP Calculus AB – Volumes with Cross Sections: Squares and Rectangles.

Questions List

Topic 8.7

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Question 1 Easy

The region bounded by the graph of a positive function ff, the x-axis, and the lines x=ax=a and x=bx=b, where a<ba<b, is the base of a solid whose cross sections perpendicular to the x-axis are squares. The solid is cut into thin slices of thickness Δx\Delta x. Which expression approximates the volume of the slice at x=xix=x_i?

Af(xi) Δxf(x_i)\,\Delta x
Bπ(f(xi))2 Δx\pi\big(f(x_i)\big)^2\,\Delta x
C(f(xi))2 Δx\big(f(x_i)\big)^2\,\Delta x
D(f(xi))2\big(f(x_i)\big)^2

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 8.7: Volumes with Cross Sections: Squares and Rectangles

Learning Objective: CHA-5.B

Calculate volumes of solids with known cross sections using definite integrals.

Essential Knowledge: CHA-5.B.1

Volumes of solids with square and rectangular cross sections can be found using definite integrals and the area formulas for these shapes.

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