The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume is 1/27 of the volume of the given cone, then what is the height above the base at which the section is made.

Given: Height of cone = 30 cm

To find: Height above the base of section.

Formula Used:

The volume of cone =

Explanation:

Given the height of the cone, H = 30 cm

Let the small cone which is cut off at a height ‘h’ from the top.

Let the radius of the big cone be R cm, and the small cone is r cm.

The volume of the big cone,

The volume of the smaller cone,

Given according to the question,

………… (1)

Now, in ∆KCB and ∆KDM

CKB = DKM (common)

KCB = KDM = 90°

∆KCB~∆KDM (by AA-similarity)

Putting the value in equation (1), we have

Thus, the height above the base at which the section is made = 30-10 = 20 cm

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