A cone of radius 10 cm is divided into two parts by drawing a plane through the mid-point of its axis parallel to its base. Compare the volume of the two parts.
Answers
Answered by
361
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
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
Attachments:
Answered by
215
like it if you like it if you like it then mark it is bring list and Like It Like It Like It Rain was like it
Attachments:
Similar questions