Let H and h be the height of cone and frustum respectively, L and l be the slant height of the same.

**Volume of frustum of a cone**

Let
H and *h* be the height of cone and frustum
respectively, *L* and *l* be the slant height of the same.

If
R, r are the radii of the circular bases of the frustum, then volume of the frustum of the cone is the difference
of the volumes of the two cones.

Since
the triangles ABC and ADE are similar, the ratio of their corresponding sides
are proportional.

**Example 7.23 **If the radii of the circular ends of
a frustum which is 45 cm high are 28 cm and 7 cm, find the volume of the
frustum.

Let
h, r and R be the height, top and bottom radii of the frustum.

Given
that, h = 45 cm, R = 28 cm, r = 7 cm

Therefore,
volume of the frustum is 48510 cm^{3}

The adjacent figure represents an oblique frustum of a cylinder.
Suppose this solid is cut by a plane through C, not parallel to the base AB,
then

where *h*_{1} and
*h*_{2} denote the greatest and
least height of the frustum.

Then its volume =

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10th Mathematics : UNIT 7 : Mensuration : Volume of frustum of a cone | Definition, Formula, Solved Example Problems | Mensuration | Mathematics

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