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Introduction to Solids of Revolution Disks & Washers

Tyler Ericson Stephen Hong. Introduction to Solids of Revolution Disks & Washers. When finding the volume of a solid revolving around the x-axis, use this formula… V = π. Solids of Revolution.

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Introduction to Solids of Revolution Disks & Washers

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  1. Tyler Ericson Stephen Hong Introduction to Solids of RevolutionDisks & Washers

  2. When finding the volume of a solid revolving around the x-axis, use this formula… V = π Solids of Revolution

  3. Find the volume of a solid of revolution obtained by rotating the first quadrant regions bounded by the curve y = x3, line x = 2 and the y-axis about the x-axis. Example 1

  4. Find the volume of a solid of revolution obtained by rotating the first quadrant regions bounded by the curve y = x3, line x = 2 and the y-axis about the x-axis. • V = π • V = π • V = π • V = π(x7/7)| • V = 128π/7 • Determine the interval and plug into formula • Simplify • Integrate and solve

  5. Find the volume of a solid of revolution obtained by rotating the first quadrant regions bounded by the curve y = 2, line x = 0 and the x=1 about the x-axis. Example 2

  6. Find the volume of a solid of revolution obtained by rotating the first quadrant regions bounded by the curve y = 2, line x = 0 and the x=1 about the x-axis. • V = π • V= π • V = π • Plug the function being rotated into the formula • Simplify

  7. Find the volume of a solid of revolution obtained by rotating the first quadrant regions bounded by the curve y = 2, line x = 0 and the x=1 about the x-axis. • V = π(2x2)| • V = π [2(12)- 2(02)] • V = 2π • Integrate the simplified solution • Solve using the given interval

  8. When you have two functions and you have to find the area of a region bounded by the two functions revolved around the x-axis use the formula: V = π Washer method

  9. Find the volume of a solid of revolution obtained by rotating the first quadrant regions bounded by the curve y = x3and line y = x around the x-axis. Example 3

  10. Find the volume of a solid of revolution obtained by rotating the first quadrant regions bounded by the curve y = x3 and line y = x around the x-axis. • x = x3 at x = 0, 1 • x is the outer function and x3 is the inner function • Determine the interval by finding where the two functions intersect • Then determine which is the inner and outer radiuses by looking at the graph

  11. Find the volume of a solid of revolution obtained by rotating the first quadrant regions bounded by the curve y = x3 and line y = x around the x-axis. • V = π • V = π • V = π(x3/3 – x7/7)| • V = π[(1/3)-(1/7)] • V = 4π/21 • Plug in the values into the formula • Simplify the integral • Integrate • Solve

  12. Always put dx at the end of your integrals Don’t forget the π!!!!! Square before subtracting when using the washer method Solids of revolution have been a FRQ topic for the past 6 years Last Reminders!!!

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