Solids cross section

40 %
60 %
Information about Solids cross section

Published on February 21, 2014

Author: roneick


Volumes of solids with known cross sections • You have already seen this being done in geometry. • For example, finding the volume of a prism , or a cylinder: • Find the area of the Base, and mutiply by the width or height.

The disk and washer method • We have also seen this in our study of Calculus via Solids of revolution • The disk and washer method use Circular cross sections • We multiply the cross sections times the width to get the actual volume.

It can really be ANY cross section • It doesn’t necessarily have to be circular. • It can be a square, triangle, ellipse, etc.. • If we can find the Area of the cross section, then we can multiple it times the width (just like before) to get the entire volume. • ANIMATION

Formulas • When the cross section is perpendicular to the x-axis, integrate with respect to x: b V A ( x ) dx a • When the cross section is perpendicular to the y-axis, integrate with respect to y: b V A ( y ) dy a

Example: • A solid is formed with a base bounded by the graphs of: f ( x) 1 x 2 x 0 g ( x) 1 x 2 Find the volume of the solid using equilateral triangle cross – sections taken perpendicular to the x-axis.


Add a comment

Related presentations

Related pages

Cross Sections INFO -

Cross Sections. A cross section is the shape we get ... In geometry it is the shape made when a solid is cut ... Cross sections are usually ...
Read more


SOLIDS, NETS, AND CROSS SECTIONS Polyhedra In this section, we will examine various three-dimensional figures, known as solids. We begin with a discussion ...
Read more

Cross sections of 3D objects | Khan Academy

Khan Academy is a nonprofit with the mission of providing a free, ... Which of the objects shown below could be sliced to create a circular cross-section?
Read more

Volumes of solids of known cross-section | Khan Academy

Volume of solids practice problems ... If you're seeing this message, it means we're having trouble loading external resources for Khan Academy.
Read more

2012 eDrawings Help - Cross Sections

Cross Sections . Create cross section planes: Use the default . XY; cross section plane. Select a plane from the Cross Section tab. Select a face in the ...
Read more

Identify Cross Sections - YouTube

Powered by Learn to identify cross sections of solids
Read more

Cross Sections - LearnZillion

In this lesson, you will learn how to visualize the 2D cross-sections of prisms by removing part of the solid.
Read more

Interactivate: Cross Section Flyer - Shodor

Cross Section Flyer: Explore cross sections of different geometric solids: cone, double cone, cylinder, pyramid, and prism. Manipulate the cross section ...
Read more

Solids of revolution cross sections worksheet - Ms. J's ...

Volumes of Solids with Known Cross-Sections Sometimes the bounded area is the base (or bottom) of a solid object. Think of a model building sitting on
Read more

Session 9, Part C: Cross Sections - Annenberg Learner

... you may want to use clay solids and dental floss to ... make as a cross section. ... Cross Sections adapted from Connected Geometry, developed by ...
Read more