 Volumes. Right Cylinder Volume of a Right Cylinder (Slices) Cross section is a right circular cylinder with volume Also obtained as a solid of revolution.

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Volumes

Right Cylinder

Volume of a Right Cylinder (Slices) Cross section is a right circular cylinder with volume Also obtained as a solid of revolution Consider the case when h=5 and r=2

Volume of a Rectangular Box Cross section is a right cylinder with volume Consider the case of a box with dimensions 3x5x7 Area of a cross section is b*l

Volume of a Sphere of radius r (slices) Cross section is a right cylinder with volume Consider the case of a sphere of radius r=3

Another Example Sketch the solid of revolution obtained by rotating around x-axis and find its volume Sketch the solid of revolution obtained by rotating around y-axis and find its volume Sketch the solid of revolution obtained by rotating around x=5 and find its volume

Volume using Shells

Example Sketch the solid of revolution obtained by rotating about x-axis and find its volume Sketch the solid of revolution obtained by rotating around y-axis and find its volume Sketch the solid of revolution obtained by rotating around x=1.2 and find its volume

Cylindrical Shells Definition of a shell Animations

Formulas Shell in general position Volume of shell

Volume Formulas Function y=f(x) Rotating about y-axis Function x=f(y) Rotating about x-axis

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