The height of a cone is 20 cm. A small cone is cut off from the top by a plane parallel to the base. If its volume be 1/125 of the volume of the original cone, determine at what height above the base the section is made.

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Solution

We have the following situation as shown in the figure

V

Let VAB be a cone of height h₁= VO₁ =20cm. Then from the symmetric triangles VO ₁A and VOA₁, we have

It is given that, volume of the cone VA₁O istimes the volume of the cone VAB. Hence, we have

Hence, the height at which the section is made is 20 − 4 = 16 cm.

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