Answer :


Let the cutting plane be passing through points B and C as shown


Height of cone = AD = H = 20 cm


Height of small cone which we get after cutting = AB = hc


Let ‘r’ be the radius of small cone we have BC = r


‘R’ be radius of original cone which is to be cut we have DE = R


From figure consider ΔABC and ΔADE


ABC = ADE = 90˚


BAC = DAE …(common angle)


as two angles are equal by AA criteria we can say that


ΔABCΔADE



Let V1 be the volume of cone to be cut


Let V2 be the volume of small cone which we get after cutting


Volume of cone = (1/3)π(radius)2(height) cm3


V1 = (1/3) × π × R2 × hc


V2 = (1/3) × π × r2 × 20


Given is that the volume of small cone is (1/8) times the original cone


V2 = (1/8) V1


(1/3) × π × r2 × 20 = (1/8) × (1/3) × π × R2 × hc



Using equation (i) we get



hc3 = 203/8 cm


hc = 20/2 cm


hc = 10 cm


But we have to find the height from base i.e. we have to find BD from figure


20 = BD + hc


20 = BD + 10


BD = 10 cm


10 cm above base the section is made.


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