Surface Area
Lateral Area + Base Area

Volume

Mass

Centroid from yz-plane
C_x

Centroid from zx-plane
C_y

Centroid from xy-plane
C_z

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.