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UPSC CDS Math Volume and Surface Area Questions
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© examsnet.com
Question : 99
Total: 104
A cone of radius r cm and height h cm is divided into two parts by drawing a plane through the middle point of its height and parallel to the base. What is the ratio of the volume of the original cone to the volume of the smaller cone ?
[2014 CDS-I]
4 : 1
8 : 1
2 : 1
6 : 1
Validate
Solution:
OB = h cm and BC = r cm
∴
O
A
=
h
2
cm
Now, ΔOAD~ΔOBC (AA similarity)
∴
AD
BC
=
OA
OB
⇒
A
D
=
r
×
(
h
2
)
2
=
r
2
Volume of original cone
Volume of smaller cone
=
1
3
π
r
2
h
1
3
π
(
r
2
)
2
h
2
=
8
Therefore, volume of original cone : Volume of smaller cone = 8 : 1
© examsnet.com
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