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KVPY SA Exam 2011 Question Paper
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© examsnet.com
Question : 63
Total: 80
The diameter of one of the bases of a truncated cone is 100 mm. If the diameter of this base is increased by 21% such that it still remains a truncated cone with the height and the other base unchanged, the volume also increases by 21%. The radius of the other base (in mm) is
65
55
45
35
Validate
Solution:
Let initially 2 bases have radii 5 cm and r cm.
Finally base have radii (1.21 × 5) and r
Ratios of volumes
=
V
2
V
1
=
1.21
V
2
=
π
h
3
[
(
6.05
)
2
+
(
6.05
)
r
+
r
2
]
V
1
=
π
h
3
[
5
2
+
5
r
+
r
2
]
V
2
V
1
=
1.21
⇒
(
6.05
)
2
+
(
6.05
)
r
+
r
2
5
2
+
5
r
+
r
2
=
1.21
⇒
r
2
=
6.3525
21
⇒
r
=
11
2
cm
=
55
mm
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