The frustum of any pyramid is the part left over if you cut off the top. We are looking at the particular case of a cone (truncate means to just cut off, so a truncated cone, is a cone that has been cut!)

Truncated Cone

To find its volume, first find the volume for the cone, and then find the volume of the smaller cone that was removed. Subtract your second value from the first.

Recall: V = 1/3 x r2h

For example

Find the volume of the frustum

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The cone has a total height of 10cm with radius 4cm.
The frustum has a height of 6cm and the top has a radius of 2cm.
That means the smaller cone we cut off has a height of 4cm and radius of 2cm.

Cone: 1/3 x 16cm2 x 10cm = 53.33cm3
Smaller Cone: 1/3 x 4cm2 x 4cm = 5.33cm3
Frustum: 53.33
cm3 - 5.33cm3 = 48cm3

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