AP Calculus AB Flashcards: Volume with Washer Method: Revolving Around Other Axes
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 10 cards to help you master important concepts.
When setting up a definite integral for volume using the washer method, what does the integrand, π(R² - r²), represent?
The integrand represents the area of a single, representative ring-shaped cross-section (the washer).
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When setting up a definite integral for volume using the washer method, what does the integrand, π(R² - r²), represent?
The integrand represents the area of a single, representative ring-shaped cross-section (the washer).
What fundamental mathematical tool is used to calculate the volumes of solids of revolution with the washer method?
Definite integrals are used to sum the areas of the infinite, infinitesimally thin, ring-shaped cross-sections to find the total volume.
What condition of the solid of revolution necessitates using the washer method instead of the simpler disk method?
The washer method is necessary when the solid has a hole in the middle, which results from a gap between the region being revolved and the axis of revolution.
What is the primary purpose of the washer method when calculating volumes?
The washer method is used to find the volumes of solids of revolution whose cross sections are ring-shaped.
If a region is revolved around the vertical line x = 5, will the definite integral be with respect to x or y?
When revolving around a vertical line, the cross-sections are horizontal rings, so the integral is set up with respect to y (i.e., dy).
What is a 'solid of revolution'?
A solid of revolution is a three-dimensional figure generated by rotating a two-dimensional planar region around a straight line (the axis of revolution).
When revolving a region around a horizontal axis, how do you determine the outer radius (R) and inner radius (r)?
The radii are the distances from the axis of revolution to the farther function (outer radius) and the nearer function (inner radius).
Can the washer method be used to find the volume of a solid revolved around a line other than the x or y-axis, such as y = -2?
Yes, the washer method can be used to find volumes of solids of revolution around any horizontal or vertical line.
What is the geometric shape of a single cross-section when using the washer method?
The cross-section is a ring, also known as a washer or an annulus.
How does changing the axis of revolution from y=0 to y=3 affect the calculation of the radii?
The radii must be recalculated as the distances from the boundary curves to the new axis y=3, not from the x-axis.