Properties of Solids

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Properties of Half Circular Conical 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


Moment of Inertia about the x₁ axis I_X1X1	Moment of Inertia about the y₁ axis I_Y1Y1	Moment of Inertia about the z₁ axis I_Z1Z1


Radius of Gyration about the x₁ axis k_X1X1	Radius of Gyration about the y₁ axis k_Y1Y1	Radius of Gyration about the z₁ axis k_Z1Z1


NOTE: AREA: Use the lateral surface area formula for the Right Circular Cone. If the shell is very thin this lateral surface area is very close the surface area of the Half Conical Shell. If it is not thin, calculate the surface area of half a Right Circular Cone (lateral + base) using the outer radius of the base circle. Then add the lateral surface area of a Right Circular Cone minus the area of the base (lateral - base) using the inner radius. VOLUME: Use the Volume formula for a Right Circular Cone. Subtract the volume calculated by using the inner radius from the volume calculated by using the outer radius. Then divide by 2. 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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