Geometry of Common Solids
Staff posted on October 23, 2006 |
Geometry of Common Solids
Properties of Cylindrical Shell
   

Surface Area
Lateral Area + Base Area

Volume

Mass

 

Centroid from yz-plane
Cx

Centroid from zx-plane
Cy

Centroid from xy-plane
Cz

 

Mass Moment of Inertia
about the x axis
Ixx

Mass Moment of Inertia
about the y axis
Iyy

Mass Moment of Inertia
about the z axis
Izz

 

Radius of Gyration
about the x axis
kxx

Radius of Gyration
about the y axis
kyy

Radius of Gyration
about the z axis
kzz

 

Moment of Inertia about the centroidal x axis ( xc )
IXcXc

Moment of Inertia about the centroidal y axis ( yc )
IYcYc

Moment of Inertia about the centroidal z axis ( zc )
IZcZc

 

Radius of Gyration about the centroidal x axis ( xc )
kXcXc

Radius of Gyration about the centroidal y axis ( yc )
kYcYc

Radius of Gyration about the centroidal z axis ( zc )
kZcZc

 

NOTE:
AREA: Use the lateral surface area formula for the Circular Cylinder. If the cylinder is very thin doubling this lateral surface area should be sufficient. If it is not, calculate the surface area of the Circular Cylinder (lateral + base) using the outer radius of the base circle. Then add the lateral surface area of a Circular Cylinder minus the area of the base (lateral - base) using the inner radius.

VOLUME: Use the Volume formula for a Circular Cylinder. Subtract the volume calculated by using the inner radius from the volume calculated by using the outer radius.

is the mass of the entire body.
is the density of the body.
is the outer radius of the body.

All of the above results assume that the body has constant density. For none constant density see the general integral forms of Mass, Mass Moment of Inertia, and Mass Radius of Gyration.

 
 
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