AP Calculus AB: Volumes: Disk and Washer Method — Drill 1

About This Drill

AP Calculus AB: Volumes: Disk and Washer Method — Drill 1 is a Math practice drill covering Disk and Washer Volumes. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

Practice setting up and evaluating volumes of revolution using the disk and washer methods. These AP Calculus AB problems require correctly squaring the radius function and identifying which curve serves as the outer versus inner radius.

Questions in This Drill

1. The region bounded by \( y = \sqrt{x} \), the x-axis, and the line \( x = 4 \) is revolved around the x-axis. Which of the following gives the volume of the resulting solid?
2. The region enclosed by \( y = x \) and \( y = x^2 \) on \( [0, 1] \) is revolved around the x-axis. Which of the following gives the volume of the resulting solid?
3. The region bounded by \( x = \sqrt{y} \), the y-axis, and the line \( y = 9 \) is revolved around the y-axis. What is the volume of the resulting solid?
4. A student attempts to find the volume of the solid formed by revolving the region between \( y = 4 \) and \( y = x^2 \) on \( [-2, 2] \) around the x-axis. The student sets up \( \pi \int_{-2}^{2} (4 - x^2)^2 \, dx \). Which of the following correctly identifies the error?
5. A solid is formed by revolving the region bounded by \( x = \sqrt{y} \) and the y-axis around the y-axis for \( 0 \leq y \leq 4 \). A cylindrical hole of radius 1 is drilled through the center of the solid along the y-axis. Which integral gives the volume of material remaining?