Q23 of 51 Page 13

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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