Chapter 6 Cross Sectional Volume

Slides:

Advertisements

Similar presentations

Section Volumes by Slicing

Advertisements

7 Applications of Integration

Disks, Washers, and Cross Sections Review

Section Volumes by Slicing

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

Volume. Find the volume of the solid formed by revolving the region bounded by the graphs y = x 3 + x + 1, y = 1, and x = 1 about the line x = 2.

SECTION 7.3 Volume. VOLUMES OF AN OBJECT WITH A KNOWN CROSS-SECTION  Think of the formula for the volume of a prism: V = Bh.  The base is a cross-section.

Volume of a Solid by Cross Section Section 5-9. Let be the region bounded by the graphs of x = y 2 and x=9. Find the volume of the solid that has as its.

5/19/2015 Perkins AP Calculus AB Day 7 Section 7.2.

Section Volumes by Slicing

V OLUMES OF SOLIDS WITH KNOWN CROSS SECTIONS 4-H.

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

Chapter 7 Quiz Calculators allowed. 1. Find the area between the functions y=x 2 and y=x 3 a) 1/3 b) 1/12 c) 7/12 d) 1/4 2. Find the area between the.

Volume of Cross-Sectional Solids

7.3.3 Volume by Cross-sectional Areas A.K.A. - Slicing.

Volume: The Disc Method

Review 7 Area between curves for x Area between curves for y Volume –area rotated –disks for x and y Volume – area rotated – washers for x and y Volume.

Let R be the region bounded by the curve y = e x/2, the y-axis and the line y = e. 1)Sketch the region R. Include points of intersection. 2) Find the.

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

Volumes by Slicing 7.3 Solids of Revolution.

Volumes by Slicing. disk Find the Volume of revolution using the disk method washer Find the volume of revolution using the washer method shell Find the.

Section Volumes by Slicing 7.3 Solids of Revolution.

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.

Volumes by Disks and Washers Or, how much toilet paper fits on one of those huge rolls, anyway??

Volumes of Solids with Known Cross Sections

Volume Find the area of a random cross section, then integrate it.

Volume of Regions with cross- sections an off shoot of Disk MethodV =  b a (π r 2 ) dr Area of each cross section (circle) * If you know the cross.

SECTION 7-3-C Volumes of Known Cross - Sections. Recall: Perpendicular to x – axis Perpendicular to y – axis.

 The volume of a known integrable cross- section area A(x) from x = a to x = b is  Common areas:  square: A = s 2 semi-circle: A = ½  r 2 equilateral.

C.2.5b – Volumes of Revolution – Method of Cylinders Calculus – Santowski 6/12/20161Calculus - Santowski.

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.

Applications of Integration

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

Super Connect 4 Integration Antigravity Game

Volumes of solids with known cross sections

Solids of Revolution Shell Method

Solids of Revolution Shell Method

7.2 Volume: The Disk Method

2.2 Multiply Polynomials Multiply a monomial and a polynomial

Finding Volumes.

Warm-Up! Find the average value of

Cross Sections Section 7.2.

Solids not generated by Revolution

Volume by Cross Sections

2.2 Multiply Polynomials Multiply a monomial and a polynomial

Review: Area betweens two curves

7 Applications of Integration

Find the volume of the solid obtained by rotating about the x-axis the region under the curve {image} from x = 2 to x = 3. Select the correct answer. {image}

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

6.4 Volumes by Cross Sections

Warmup 1) 2) 3).

Volume of Solids with Known Cross Sections

Volume by Cross-sectional Areas A.K.A. - Slicing

Applications Of The Definite Integral

7 Applications of Integration

6.2a DISKS METHOD (SOLIDS OF REVOLUTION)

7 Applications of Integration

Warm Up Find the volume of the following shapes (cubic inches)

Area & Volume Chapter 6.1 & 6.2 February 20, 2007.

Warm Up Draw the graph and identify the axis of rotation that

Copyright © Cengage Learning. All rights reserved.

Calculus 5.9: Volume of a Solid by Plane Slicing

Section Volumes by Slicing

Warm Up Find the volume of the following 3 dimensional shapes.

AP problem back ch 7: skip # 7

7 Applications of Integration

Presentation transcript:

Chapter 6 Cross Sectional Volume 1.) Draw a cross section perpendicular to the x-axis. Write an expression that represents the length of that cross section. This is a “cross-section”. A “cross-section” goes across the section. 5/3/2019

Chapter 6 Cross Sectional Volume 2.) Draw a cross section perpendicular to the y-axis. Write an expression that represents the length of that cross section. 5/3/2019

Chapter 6 Cross Sectional Volume Let R be the region in the first quadrant bounded by the graph of the horizontal line y = 6, the y-axis, and as shown in the figure. 3.) Region R is the base of a solid. For each x, where 0 ≤ x≤ 9, the cross section of the solid taken perpendicular to the x-axis is a square. Write, but do not evaluate, an integral expression that gives the volume of the solid. 5/3/2019

Chapter 6 Cross Sectional Volume Let R be the region in the first quadrant bounded by the graph of the horizontal line y = 6, the y-axis, and as shown in the figure. 4.) Region R is the base of a solid. Cross sections of the solid, perpendicular to the x-axis, are semicircles. Write, but do not evaluate, an integral expression that gives the volume of the solid. 5/3/2019

Chapter 6 Cross Sectional Volume Let R be the region in the first quadrant bounded by the graph of the horizontal line y = 6, the y-axis, and as shown in the figure. 5.) Region R is the base of a solid. For each y, where 0 ≤ y ≤ 6, the cross section of the solid taken perpendicular to the y-axis is a rectangle whose height is 3 times the length of its base in region R. Write, but do not evaluate, an integral expression that gives the volume of the solid. 5/3/2019

Chapter 6 Cross Sectional Volume Let R be the region in the first quadrant bounded by the graph of the horizontal line y = 6, the y-axis, and as shown in the figure. 6.) Region R is the base of a solid. Cross sections of the solid, perpendicular to the y-axis, are semicircles. Write, but do not evaluate, an integral expression that gives the volume of the solid. 5/3/2019

Chapter 6 Cross Sectional Volume p.430 #’s 57, 59, 60, 61 5/3/2019