Volume with Disc Method: Revolving Around Other Axes

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Study Guide Overview

This study guide covers the disc method for finding volumes of solids of revolution, specifically focusing on rotations around axes other than the x and y-axes. It explains how to set up and solve integrals representing the volume, emphasizing the importance of visualizing the rotation and determining the correct variable of integration (x or y) based on the axis of rotation (horizontal or vertical). The guide provides the general integral formulas for both horizontal (y=b) and vertical (x=a) axes of rotation and includes a practice problem and solution involving rotating a region around a horizontal line.

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Previous Topic - Volume with Disc Method: Revolving Around the x- or y-Axis Next Topic - Volume with Washer Method: Revolving Around the x- or y-Axis

Question 1 of 9

🎉 If a region is revolved around the line $y = 4$ , which of the following integrals would be used to calculate the volume using the disc method?

$\int_{a}^{b} \pi (f(x) - 4)^2 dx$

$\int_{a}^{b} \pi (f(y) - 4)^2 dy$

$\int_{a}^{b} \pi (f(x))^2 dx$

$\int_{a}^{b} \pi (4 - f(x))^2 dx$

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Volume with Disc Method: Revolving Around Other Axes

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