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3-D Frustum of Cone Formula

In geometry, a frustum is the portion of a solid normally a cone or pyramid which lies between two parallel planes cutting it. A bucket is an everyday example of a conical frustum. The bottom internal diameter is usually smaller than the upper internal diameter.

A frustum may be formed from a cone with a circular base by cutting off the tip of the cone with a cut perpendicular to the height, forming a lower base and an upper base that are circular and parallel. The volume of a conical or pyramidal frustum is the difference between the volumes of the solid before slicing the apex off, minus the volume of the part that was sliced off:

V = \frac{h_2 B_2 - h_1 B_1}{3}

where B1 is the area of the smaller base, B2 is the area of the larger base, and h1, h2 are the perpendicular heights from the apex to the planes of the two bases.

Considering that

\frac{B_1}{h_1^2}=\frac{B_2}{h_2^2}

The volume can also be expressed as the product of the height h = h2−h1 of the frustum and the Heronian mean of their areas:

V = \frac{h}{3}(B_1+B_2+\sqrt{B_1 B_2})

The part of a right circular cone between the base and a plane parallel to the base whose distance from the base is less than the height of the cone.

Height: h
     Radius of bases: r, R
     Slant height: s
     Lateral surface area: S
     Total surface area: T
     Volume: V

          s = sqrt([R-r]2+h2)
          S = Pi(r+R)s
          T = Pi(r[r+s]+R[R+s])
          V = Pi(R2+rR+r2)h/3  

Frustum of Cone Formula

 
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