7.2 Volume: The Disk Method

Slides:

Advertisements

Similar presentations

7 Applications of Integration

Advertisements

Find the exact volume of the solid formed by revolving the region enclosed by the following functions around the x-axis. Specify whether you are using.

DO NOW: Find the volume of the solid generated when the

Disks, Washers, and Cross Sections Review

More on Volumes & Average Function Value. Average On the last test (2), the average of the test was: FYI - there were 35 who scored a 9 or 10, which means.

Applications of Integration Copyright © Cengage Learning. All rights reserved.

Solids of Revolution Washer Method

Volumes – The Disk Method Lesson 7.2. Revolving a Function Consider a function f(x) on the interval [a, b] Now consider revolving that segment of curve.

The Disk Method (7.2) April 17th, I. The Disk Method Def. If a region in the coordinate plane is revolved about a line, called the axis of revolution,

Miss Battaglia AP Calculus. Rotate around the x-axis and find the volume of y= 1 / 2 x from 0 to 4.

TOPIC APPLICATIONS VOLUME BY INTEGRATION. define what a solid of revolution is decide which method will best determine the volume of the solid apply the.

Section 6.2.  Solids of Revolution – if a region in the plane is revolved about a line “line-axis of revolution”  Simplest Solid – right circular cylinder.

S OLIDS OF R EVOLUTION 4-G. Disk method Find Volume – Disk Method Revolve about a horizontal axis Slice perpendicular to axis – slices vertical Integrate.

Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, B Volumes by the Washer Method Limerick Nuclear Generating Station,

Section 7.2 Solids of Revolution. 1 st Day Solids with Known Cross Sections.

A solid of revolution is a solid obtained by rotating a region in the plane about an axis. The sphere and right circular cone are familiar examples of.

Chapter 5: Integration and Its Applications

Volume: The Disc Method

Volumes Lesson 6.2.

6.3 Volumes of Revolution Tues Dec 15 Do Now Find the volume of the solid whose base is the region enclosed by y = x^2 and y = 3, and whose cross sections.

6.2 Volumes on a Base.

Solids of Known Cross Section. Variation on Disc Method  With the disc method, you can find the volume of a solid having a circular cross section  The.

C YLINDRICAL SHELLS C ONTINUED 4-Jcont Comparison of Methods.

6.3 Volumes of Revolution Fri Feb 26 Do Now Find the volume of the solid whose base is the region enclosed by y = x^2 and y = 3, and whose cross sections.

Calculus 6-R Unit 6 Applications of Integration Review Problems.

7.2 Volume: The Disk Method (Day 3) (Volume of Solids with known Cross- Sections) Objectives: -Students will find the volume of a solid of revolution using.

7-2 SOLIDS OF REVOLUTION Rizzi – Calc BC. UM…WHAT?  A region rotated about an axis creates a solid of revolution  Visualization Visualization.

Volume by the Disc/Washer Method. The disc/washer method requires you to visualize a series of discs or washers, compute their volume and add the volumes.

Applications of Integration

The Disk Method (7.2) February 14th, 2017.

FINDING VOLUME USING DISK METHOD & WASHER METHOD

Volume: The Disk Method

Solids of Revolution Shell Method

Solids of Revolution Shell Method

The Shell Method Section 7.3.

Finding Volumes Chapter 6.2 February 22, 2007.

Finding Volumes Disk/Washer/Shell

Review of Area: Measuring a length.

Volumes – The Disk Method

Cross Sections Section 7.2.

Volume by Cross Sections

Section 6.2 ∆ Volumes Solids of Revolution Two types: Disks Washers.

AP Calculus Honors Ms. Olifer

Review: Area betweens two curves

Volumes – The Disk Method

7 Applications of Integration

Volumes of Solids of Revolution

Find the volume of the solid obtained by rotating the region bounded by {image} and {image} about the x-axis. 1. {image}

Chapter 7.2: Volume The Disk Method The Washer Method Cross-sections

7.3 Volume: The Shell Method

6.2 Volumes If a region in the plane is revolved about a line, the resulting solid is called a solid of revolution, the line is called the axis of revolution.

Warm up Find the area of surface formed by revolving the graph of f(x) = 6x3 on the interval [0, 4] about the x-axis.

7 Applications of Integration

Volume - The Disk Method

6.2a DISKS METHOD (SOLIDS OF REVOLUTION)

7 Applications of Integration

Volumes of Revolution The Shell Method

AP Calculus AB Day 3 Section 7.2 5/7/2019 Perkins.

6.1 Areas Between Curves To find the area:

Section 7.2 Day 2 Disk Method

6.2 Solids of Revolution-Disk Method Warm Up

Copyright © Cengage Learning. All rights reserved.

Review 6.1, 6.2, 6.4.

Section Volumes by Slicing

Section 7.2 Day 5 Cross Sections

Solids of Revolution PART DEUX: WaShErS Rita Korsunsky

Applications of Integration

Volumes of Revolution: Disk and Washer Method

6.3 – Volumes By Cylindrical Shells

7 Applications of Integration

Presentation transcript:

7.2 Volume: The Disk Method

The Disk Method Horizontal Axis of Revolution Vertical Axis of Revolution

Using the Disk Method Find the volume of the solid formed by revolving the region bounded by the graph of f(x) and the x-axis about the x-axis.

Revolving About a Line That is Not a Coordinate Axis Find the volume of the solid formed by revolving the region bounded by f(x) and g(x) and the line y=1.

The Washer Method

Using the Washer Method Find the volume of the solid formed by revolving the region bounded by the following graphs about the x-axis.

Integrating with Respect to y, Two-Integral Case Find the volume of the solid formed by revolving the region bounded by the following graphs about the y-axis.

Manufacturing A manufacturer drills a hole through the center of a metal sphere of radius 5 inches. The hole has a radius of 3 inches. What is the volume of the resulting metal ring?

Solids of Known Cross Sections

Triangular Cross Sections Find the volume of the solid. The base of the solid is the regions bounded by the lines: The cross sections perpendicular to the x-axis are equilateral triangles.