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If a cone of radius 10cm is divided into two parts by drawing a plane through the mid points of its axis, parallel to its base. Compare the volumes of the two parts.

If a cone of radius 10cm is divided into two parts by drawing a plane through the mid points of its axis, parallel to its base. Compare the volumes of the two parts.

Grade:10

1 Answers

Arun
25750 Points
6 years ago
Dear student
 
As the cone is divided into two equal parts by the axis so, AQ = AP/2
with the help of similarity theory,
QD / PC = AQ / AP 
so, QD / PC = 1/2
so, rdius of QD = PC/2 = R/2
now,the volume of frustum = 1/3πR²H - 1/3π(R/2)²(H/2)
                                                = 1/3πR²H*7/8
compare the two parts in cone 
1st is the volume of small cone and 2nd the volume of frustum 
i.e. (1/3π(R/2)²(H/2))/(1/3πR²H*7/8) = (1/8)/(7/8)=1/7
 
 
Regards
Arun (askIITians forum expert)

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