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.

Slides:

Advertisements

Similar presentations

Section Volumes by Slicing

Advertisements

7 Applications of Integration

Disks, Washers, and Cross Sections Review

Section Volumes by Slicing

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.

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.

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.

Finding Volumes.

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

Section Volumes by Slicing

6.2C Volumes by Slicing with Known Cross-Sections.

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

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

Cross Sections By: Meghan Grubb. What are cross sections? A cross sectional area results from the intersection of a solid with a plane, usually an x-y.

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.

7.3 Day One: Volumes by Slicing. Volumes by slicing can be found by adding up each slice of the solid as the thickness of the slices gets smaller and.

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

DO NOW!!! (1 st ) 1.A rectangular prism has length 4 cm, width 5 cm, and height 9 cm. a) Find the area of the cross section parallel to the base. b) Find.

Volume: The Disc Method

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.

Finding Volumes Chapter 6.2 February 22, In General: Vertical Cut:Horizontal Cut:

Volumes Lesson 6.2.

Volumes by Slicing 7.3 Solids of Revolution.

Area of Composite Figures

Area of Composite Figures

Finding Volumes. In General: Vertical Cut:Horizontal Cut:

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.

6.2 Volumes on a Base.

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.

Ch. 8 – Applications of Definite Integrals 8.3 – Volumes.

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.

6.2 - Volumes Roshan. What is Volume? What do we mean by the volume of a solid? How do we know that the volume of a sphere of radius r is 4πr 3 /3 ? How.

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.

9.1 PERIMETER AND AREA OF PARALLELOGRAMS Objective: Students find the perimeter and area of parallelograms.

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.

Section 7.3: Volume The Last One!!! Objective: Students will be able to… Find the volume of an object using one of the following methods: slicing, disk,

Applications of Integration

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

Volumes of solids with known cross sections

Area of Shapes.

Finding Volumes.

Finding Volumes Chapter 6.2 February 22, 2007.

Cross Sections Section 7.2.

Solids not generated by Revolution

Volume by Cross Sections

7 Applications of Integration

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

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

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.

Chapter 6 Cross Sectional Volume

Area of Composite Figures

Copyright © Cengage Learning. All rights reserved.

Section Volumes by Slicing

Section 7.2 Day 5 Cross Sections

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

AP problem back ch 7: skip # 7

Presentation transcript:

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 base if every cross section by a plane perpendicular to the x-axis has the given shape. A square

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 base if every cross section by a plane perpendicular to the x-axis has the given shape. A rectangle of height 2

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 base if every cross section by a plane perpendicular to the x-axis has the given shape. A semicircle

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 base if every cross section by a plane perpendicular to the x-axis has the given shape. A quarter circle

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 base if every cross section by a plane perpendicular to the x-axis has the given shape. An equilateral triangle

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 base if every cross section by a plane perpendicular to the x-axis has the given shape. A triangle with height equal to ¼ the length of the base.

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 base if every cross section by a plane perpendicular to the x-axis has the given shape. A trapezoid with lower base in the xy-plane, upper base equal to ½ the length of the lower base, and height equal to ¼ the length of the lower base.