'Washer method' presentation slideshows

DO NOW: Find the volume of the solid generated when the r egion in the first quadrant bounded by the given curve and line i s revolved about the x -axis. (2,25). Cross-section area:. (0,5). Volume:. f (x). x. The Washer Method. Section 7.3c.

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.

Washer Method. What if cross sectional area created is not a disc?. Find the volume when the region enclosed by y = x and y = x 2 is rotated about the x-axis? - creates a horn shaped cone - area of the cone will be the outside area minus the inside area – shape of a washer. Example.

Lecture 1 – Volumes . Area – the entire 2-D region was sliced into strips Before width( x) was introduced, only dealing with length. f(x). a. b. Volume – same concept, 3-D solid is sliced into strips Before width is introduced, only dealing with 2-D area. Solids of revolution. f(x).

Washer Method. Washer Method. Washer Method. Washer Method.

Warm Up. 8.3B – Volume of Solids. Goal: Use the disk and washer method to find volumes. . Take Notes on the video below. http:// education-portal.com/academy/lesson/how-to-find-volumes-of-revolution-with-integration.html#lesson. Example 1. Suppose I start with this curve.

Review Chapter 6. 1. Beginning AP Problem 2. Homework 3. Review/Homework Assignment 4. Review Limits. AGENDA. Find the area of the region bounded by the graphs of and 8. #1. Find the area of the region bounded by the graphs of and 125/6 .

Volumes of Revolution: Disk and Washer Method. AP Calculus. Volume of Revolution: Method. Lengths of Segments: In revolving solids about a line, the lengths of several segments are needed for the radii of disks, washers, and for the heights of cylinders. A). DISKS AND WASHERS

Photo by Vickie Kelly, 2003. Greg Kelly, Hanford High School, Richland, Washington. 7.2 day 1. Disk Method. Limerick Nuclear Generating Station, Pottstown, Pennsylvania. Suppose I start with this curve.

Applications of Integration. Volumes of Revolution Many thanks to http:// mathdemos.gcsu.edu / shellmethod /gallery/ gallery.html. Method of discs. Take this ordinary line. Revolve this line around the x axis. 2. 5. We form a cylinder of volume.

Applications of Integration. Hanna Kim & Agatha Wuh Block A. Disk Method Intro. Disk Method is in many ways similar to cutting a rollcake into infinitely thin pieces and adding all of them together to find out the volume of the whole. Delving into Disk Method. Disk = right cylinder

Section 7.2. Solids of Revolution. 1 st Day. Solids with Known Cross Sections. 1. Method of Slicing. Sketch the solid and a typical cross section. Find a formula for A ( x ) = the area of a cross section.

Lesson Notes 6.5. Disks, Washers and Shells* * BC Topic. Greg Kelly, Hanford High School, Richland, Washington. Example #1 Suppose you start with this curve. Your boss at the ACME Rocket Company has assigned you to build a nose cone in this shape.

Photo by Vickie Kelly, 2003. Greg Kelly, Hanford High School, Richland, Washington. 7.3 day 2. Disks, Washers and Shells. Limerick Nuclear Generating Station, Pottstown, Pennsylvania. Suppose I start with this curve.

Photo by Vickie Kelly, 2003. Greg Kelly, Hanford High School, Richland, Washington. 7.3 day 2. Disk and Washer Methods. Limerick Nuclear Generating Station, Pottstown, Pennsylvania. Suppose I start with this curve.

Section 6.2: Volumes. Practice HW from Stewart Textbook (not to hand in) p. 457 # 1-13 odd. Solids of Revolution. In this section, we want to examine how to find the volume of a solid of revolution, which is formed by rotating a region in a plane about a line.

6.3 Shell Method. HW pg 432 2-10, 14 (even). Find the volume of the region bounded by , , and revolved about the y -axis. We can use the washer method if we split it into two parts:. cylinder. inner radius. outer radius. thickness of slice.

Application of Definite Integrals. Dr. Farhana Shaheen Assistant Professor YUC- Women Campus. Calculus ( Latin , calculus , a small stone used for counting).

Jeffrey Santos. AP Calculus FRQ Year 2008 #5. The Question?. A.) Find the Area of R. Using the graphing calculator, we find the intersection points of y=lnx and y=x-2. The intersection points of the graph are when x=.15859 and 3.14619. (Let A=.15859 and B=3.14619). Which then equals to:.

Volumes Using Cross-Sections. Solids. Solids not generated by Revolution. Solids of Revolution. Examples: Classify the solids. Volumes Using Cross-Sections. Solids. Solids not generated by Revolution. Solids of Revolution. Volumes Using Cross-Sections. Solids of Revolution.