Volume Homework Help

Get customized homework help now!

Volume:The Shell Method

Instead of taking small elements of area like a rectangle, we need to map out a small element of volume, which is equal to the cross-sectional area multiplied by our interval Δx. Then we'll sum them all up to find the total volume of the solid. There are several ways to come up with this element of volume, but only two are really important to this class:

  • The disc method
  • The shell method

The "Shell" method

The shell method is a method that can be used when the disc method becomes difficult to use, such as with very complex shapes.

However, there are tighter restrictions on when you can use the Shell method:

  • It can only be used if the shape is SYMMETRICAL around some axis.
  • It can only be used if the shape is CIRCULAR around the axis perpendicular to its symmetry.

For instance, a cylinder is a great candidate for the shell method. It is symmetrical from the side, and it is circular around the axis perpendicular to its side (the top). Additionally, volumes of revolution always fulfill these requirements.

The shell method is similar to the disc method in that we're defining an element of volume and then summing them up.(an integral). But, instead of discs, we're defining thin, cylindrical shells.

To find the volume of a solid of revolution with the shell method, use on of the following.
Horizontal axis of revolution; Vertical axis of revolution

The cylinder method is used when the slice that was drawn is parallel to the axis of revolution; i.e. when integrating perpendicular to the axis of revolution. A method of computing the volume of a solid of revolution by integrating over the volumes of infinitesimal shell-shaped sections bounded by cylinders with the same axis of revolution as the solid. The best way to compute the volume by this method would be to first compute the volume corresponding to the region bounded by y1 and the x-axis, and then to subtract out the volume of rotation of the region between y2 and the x-axis.

Classof1.com is a pioneer in online tutoring and homework help. Our tutors are highly qualified in their subject areas and have been helping students since 2003. For immediate Volume homework help, use the homework-help form present on this page. You can also get help with your Volume homework by writing to learning@classof1.com.

For instant assistance, click here to start a live-chat with us.

back to school with Free Amazon gift Card upto $50
Math Homework Help
Name* :
Email* :
Country* :
Phone* :
Subject* :
Attachment* :
Upload another homework (upto 5 uploads max.)

Type Your Questions OR Instructions Below
Type this code and send us your volume homework questions to get written lessons from expert volume tutors.
(Type Security Code - case sensitive)
By clicking on the "Get Homework Help" button, you agree to the Terms and Conditions of Classof1.
Courses/Topics we help on
Discrete Mathematics Applied Calculus I Applied Calculus II
Healthcare Statistics and Research Advanced Engineering Mathematics I
Advanced Engineering Mathematics II
Introduction to Algebra Basic Algebra Algebra for College Students
Algebra for College Students Pre-Calculus Statistics for Decision-Making
Polar Co-ordinates Area in Polar Coordinates Solving Systems of Equations
Systems of Inequalities Quadratic Equations Matrices and System of Equations
The Determinant of a Square Matrix Cramer's Rule Ellipse
Hyperbola Rate of Change Measurement of Speed
Finding Limits Graphically Higher Order Derivatives Rolle's Theorem and Mean Value Theorem
Concavity and Second Derivative Test Limits at Infinity Indefinite Integration
Definite Integration Integration by Substitution Area of a Region Between Two Curves
Volume by Shell Method and Disc Method Integration by Parts Trigonometric Integration
Differential Equations Slope Fields Growth and Decay
System of Differential Equations Parametric Equations Complex Numbers
The Inverse of a Square Matrix Parabola Functions and Their Graphs
Evaluating Limits Analytically Increasing and Decreasing Functions Newton's Method
Finding Area Using Integration Numerical Integration Moments
Partial Fractions Separation of Variables Second Order Differential Equations
IB Maths    
Classof1.com is a safe, secure and trusted website as certified by Norton Secure (powered by VeriSign)
About Us | Terms of Use | Privacy Policy Copyright © 2002-2014 Classof1. All rights reserved.
Live chat assistance with volume homework help
Live chat assistance with volume homework help