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  3. AP Maths
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Volumes of Revolution

Emily Davis

Emily Davis

5 min read

Next Topic - Washer Method Around Other Axes
Study Guide Overview

This study guide covers the washer method for finding the volume of revolution around the y-axis. It explains the step-by-step methodology including identifying functions, setting up the integral with respect to y, rewriting functions in terms of y, and determining integration boundaries. It provides a worked example, practice questions, and a glossary of key terms like washer method, volume of revolution, and integral. Key takeaways emphasize rewriting functions, correct integration, and boundary identification.

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Previous Topic - Washer Method Around the x-AxisNext Topic - Washer Method Around Other Axes

Question 1 of 9

Ready to find some volumes? 🚀 What is the general formula for the volume of a solid of revolution around the y-axis using the Washer Method, where x1(y)x_1(y)x1​(y) and x2(y)x_2(y)x2​(y) are the inner and outer radii, respectively, and the region is bounded by y=ay=ay=a and y=by=by=b?

V=π∫ab(x2(y)−x1(y))2,dyV = \pi \int_{a}^{b} (x_2(y) - x_1(y))^2 , dyV=π∫ab​(x2​(y)−x1​(y))2,dy

V=π∫ab(x22(y)−x12(y)),dyV = \pi \int_{a}^{b} (x_2^2(y) - x_1^2(y)) , dyV=π∫ab​(x22​(y)−x12​(y)),dy

V=∫ab(x22(y)−x12(y)),dyV = \int_{a}^{b} (x_2^2(y) - x_1^2(y)) , dyV=∫ab​(x22​(y)−x12​(y)),dy

V=2π∫aby(x2(y)−x1(y)),dyV = 2\pi \int_{a}^{b} y(x_2(y) - x_1(y)) , dyV=2π∫ab​y(x2​(y)−x1​(y)),dy