What is the formula for finding the volume of a solid of revolution when rotated about the y-axis?

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∻Solution by Steps∻ ‖ step 1 ⋮ To find the volume of a solid of revolution when rotated about the y-axis, we use the disk or washer method. ‖ ‖ step 2 ⋮ The formula for the volume $V$ using the disk method is $V = \pi \int_{a}^{b} [R(y)]^2 dy$, where $R(y)$ is the radius of the disk at a particular $y$ value, and $a$ and $b$ are the bounds of integration on the y-axis. ‖ ‖ step 3 ⋮ If there is an inner radius $r(y)$, creating a hollow center (washer), the formula is modified to $V = \pi \int_{a}^{b} ([R(y)]^2 - [r(y)]^2) dy$. ‖ ∻Answer∻ ⚹ The formula for the volume of a solid of revolution when rotated about the y-axis is $V = \pi \int_{a}^{b} [R(y)]^2 dy$ for a solid disk, and $V = \pi \int_{a}^{b} ([R(y)]^2 - [r(y)]^2) dy$ for a washer. ⚹ ∻Key Concept∻ ⚹Disk and Washer Methods⚹ ∻Explanation∻ ⚹The disk method calculates the volume of a solid by integrating the area of circular disks, while the washer method accounts for a hollow center by subtracting the area of the inner disk from the outer disk.⚹◊What is the formula for finding the volume of a solid of revolution when rotated about the y-axis in terms of cylindrical shells?⍭ Generate me a similar question◊

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