This session shows frustum of a Cone in I/GCSE Mathematics.

Frustum of a Cone

Frustum of cone is the part of cone when it is cut by a plane into two parts. The upper part of cone remains same in shape but the bottom part makes a frustum. To get this part of the right circular cone we have to slice it horizontally or parallel to the base. Both pieces have different volumes and areas.

## Volume

In the cone given above, the frustum can be considered as the difference of two right circular cones.

Let the larger cone which has a height equal to “h” units, slant height as “l” units and radius as “r” units be named as cone 1 and the smaller right circular cone be named as cone 2 whose height is given as h’ units, radius as r’ units and the slant height as l’ units.

When it comes to I/GCSE Mathematics, the height of frustum is”H” units and its slant height is “L” units.

Similarly,

Therefore, the volume of the frustum of cone can be given as:

From the figure given above, in the ∆OO’D and ∆OPB;

Hence, In I/GCSE Mathematics, according to condition for similar triangles the ratio of corresponding sides must be equal:

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