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Truncated cone
If a straight circular cone is intersected by a plane parallel to its base - domyhomework , the result is a straight truncated cone. The parallel surfaces AG and AD are similar circles.
If a straight circular cone is intersected by a plane parallel to the base, the result is a straight circular truncated cone (in short: truncated cone) and a supplementary cone - math problem solver . The parallel surfaces AG and AD are circles similar to each other. The following applies to the base surface and the top surface:
AG:AD=h 1^2:h 2^2
h 1 is the height of the complete cone, h 2 the height of the supplementary cone. Furthermore, the following applies to the length of the side edge s of the truncated cone:
s^2=(r2- r1)^2+ h^2
If the lateral surface of a straight circular cone is unwound in a plane, the result is the section of a circular ring - geometry homework help . The surface area of this circular ring section corresponds to the surface area of the mantle of the truncated cone.
A M=π s(r 2+r 1)=1/2π s(d 2+d 1)
For the surface area of the straight frustum of the cone then holds:
A O=π[r2^2+r1^2+s(r 2+r 1)]
The volume of the truncated cone is the difference between the volumes of the circular cone and the supplementary cone. The following then applies to the volume of the truncated cone:
V=1/3(AG⋅h1-AD⋅h2)
V=1/3h(AG+√(AG AD)+AD)
V=1/3π h(r 2^2+r 2 r 1+r 1^2)
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