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UPSC CDS Math Volume and Surface Area Questions
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© examsnet.com
Question : 54
Total: 104
The height of a cone is 60 cm. A small cone is cut off at the top by a plane parallel to the base and its volume is
1
64
the volume of original cone. What is the height from the base at which the section is made ?
[2016 CDS-II]
15 cm
20 cm
30 cm
45 cm
Validate
Solution:
Let r and h be the radius and height of the small cone, respectively.
Suppose the radius of the original cone is R.
Now αOAB ~ ΔOCD
∴
O
A
O
C
=
A
B
C
D
⇒
h
60
=
r
R
....(1)
Volume of the smaller cone
=
1
64
×
Volume of the original cone
∴
1
3
π
r
2
h
1
3
π
R
2
×
60
=
1
64
⇒
(
r
R
)
2
×
h
60
=
1
64
⇒
(
h
60
)
3
=
(
1
4
)
3
[Using (1)
⇒
h
=
15
c
m
Height from the base at which the section is made = 60 – 15 = 45 cm
© examsnet.com
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