Volumes of Revolution: Disk Method

Volumes of Revolution: Disk Method

VOLUMES OF REVOLUTION Honors Calculus Keeper 38 THE DISK METHOD To find the volume of a solid of revolution with the disk

method, use one of the following: Horizontal Axis of Revolution Vertical Axis of Revolution EXAMPLE

Find the volume of the solid formed by revolving the region bounded by the graph of and about the . EXAMPLE

Find the volume of the solid formed by revolving the region bounded by the graph of and about the . EXAMPLE

Find the volume of the solid formed by revolving the region bounded by the graph of and about the line . EXAMPLE

Find the volume of the solid formed by revolving the region bounded by the graph of and the about the . EXAMPLE

Find the volume of the solid formed by revolving the region bounded by the graph of and the about the line . EXAMPLE

Determine the volume of the solid by rotating the region bounded by and the about the . THE WASHER METHOD Use the washer method for solids of revolution with holes.

EXAMPLE Determine the volume of the solid by rotating the portion of the region bounded by and that lies in the first quadrant about the .

EXAMPLE Determine the volume of the solid by rotating the region bounded by and about the line .

EXAMPLE Determine the volume of the solid by rotating the region bounded by and about the line .

EXAMPLE Find the volume of the solid formed by revolving the region bounded by the graphs of and about the x-axis.

Recently Viewed Presentations

  • Discovering Diversity Advantages of learning and living in

    Discovering Diversity Advantages of learning and living in

    Arial MS Pゴシック Franklin Gothic Demi Blank Presentation Adobe Photoshop Image Microsoft Graph 2000 Chart Microsoft Graph Chart Discovering Diversity Welcome to ASU ASU 101 Small Class Experience Diversity at ASU Diversity as representation Diversity as inclusion Diversity at ASU...
  • Opinions on 19th Century Imperialism

    Opinions on 19th Century Imperialism

    This platform ( belief of all party members) in response to U.S occupation of Cuba, Puerto Rico and the Philippines after the Spanish-American War identifies that imperialism is "hostile to liberty and tends toward militarism" it invoke enlightened ideals "...
  • Aberdeen Latin American Income Fund Limited

    Aberdeen Latin American Income Fund Limited

    Unlike income from a single bond, the level of income from an investment trust is not fixed and may fluctuate. • With funds investing in bonds there is a risk that interest rate fluctuations could affect the capital value of...
  • Student Assessment Update, Board of Elementary and Secondary ...

    Student Assessment Update, Board of Elementary and Secondary ...

    Massachusetts Department of Elementary and Secondary Education. Today's Agenda. ... $5M released for IT Bond Grant. E-rate reform. ... Carrie Conaway, Associate Commissioner, Research, Planning, and Delivery.
  • STAAR Review 8  Interactions between animal systems  Interactions

    STAAR Review 8 Interactions between animal systems Interactions

    The dermal tissue is the outer covering of the plant that serves as a protective barrier. Ground tissue is responsible for carrying out most of the plant's metabolic functions, such as photosynthesis. Vascular tissue transports needed substances throughout the plant,...
  • www.rc.usf.edu

    www.rc.usf.edu

    Author: Autar Kaw Last modified by: Kaw, Autar Created Date: 1/18/2008 12:25:06 AM Document presentation format: On-screen Show (4:3) Company: Engineering Computing
  • Session 5: Lion tamers and horse whisperers - shaping ...

    Session 5: Lion tamers and horse whisperers - shaping ...

    Allow people to follow their conscience. There is little research data to support Anne Frank's dictum that 'most people are good at heart', but most of us prefer to believe it. When there is an explicit expectation that the workplace...
  • La pauvreté multidimensionnelle en République du Congo ...

    La pauvreté multidimensionnelle en République du Congo ...

    La pauvreté multidimensionnelle des femmes et des enfants en République du Congo Bethuel Makosso Université Marien Ngouabi Alain Mpoué Centre national de la statistique et des études économiques (CNSEE)