Properties of Solids

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Properties of Spherical Shell
Centroid from yz-plane C_x	Centroid from zx-plane C_y	Centroid from xy-plane C_z


Surface Area Lateral Area + Base Area	Volume	Mass


Mass Moment of Inertia about the x axis I_xx	Mass Moment of Inertia about the y axis I_yy	Mass Moment of Inertia about the z axis I_zz


Radius of Gyration about the x axis k_xx	Radius of Gyration about the y axis k_yy	Radius of Gyration about the z axis k_zz


Moment of Inertia about the centroidal x axis ( x_c ) I_XcXc	Moment of Inertia about the centroidal y axis ( y_c ) I_YcYc	Moment of Inertia about the centroidal z axis ( z_c ) I_ZcZc


Radius of Gyration about the centroidal x axis ( x_c ) k_XcXc	Radius of Gyration about the centroidal y axis ( y_c ) k_YcYc	Radius of Gyration about the centroidal z axis ( z_c ) k_ZcZc


NOTE: is the mass of the body. All equations use the outer radius of the shell. is the thickness of the shell and is assumed small. is the density of the body. If , the approximate calculated volume is no more than 10.7% larger than the exact volume. For exact results use the Sphere equations for the outer and inner radii. 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.