A cone with its top sliced off by a plane parallel to the base: a bucket, a glass, a lampshade.
3 lessons, about 1 h 35 min3 simulations10 problems6 practice questionsPython in every lesson
Created by StemPy LabA frustum is what is left of a cone when its top is cut off by a plane parallel to the base. Its slant height comes from a right triangle, and similar triangles give the complete cone that it was cut from.
The curved surface of a frustum is pi times the sum of the radii times the slant height. The volume is pi times the height over three times a bracket of three terms. Both come from subtracting a small cone from the complete cone.
Word problems on buckets, glasses and lampshades use the slant height, the curved surface and the volume of a frustum. A cone cut by a plane parallel to its base gives a small cone and a frustum with volumes in the ratio of cubes and areas in squares.
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