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Standard IX
Mathematics
Volume of a right circular cone
Question
If h, C and V respectively are the height, the curved surface and volume of cone, then
3
π
V
h
3
−
C
2
h
2
+
9
V
2
is?
4
π
r
0
2
π
r
h
π
r
3
A
2
π
r
h
B
0
C
4
π
r
D
π
r
3
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Solution
Verified by Toppr
Given,
r
,
h
,
l
,
C
,
V
are radius, height, slant height, curved surface and volume of cone, respectively.
We know, volume of the cone
V
=
1
3
π
r
2
h
and curved surface
C
=
π
r
l
=
π
r
√
h
2
+
r
2
Then,
3
π
V
h
3
−
C
2
h
2
+
9
V
2
⟹
3
π
(
1
3
π
r
2
h
)
h
3
−
(
π
r
√
h
2
+
r
2
)
h
2
+
9
(
1
3
π
r
2
h
)
2
⟹
π
2
r
2
h
4
−
π
2
r
2
h
4
−
π
2
r
2
h
4
+
π
2
r
2
h
4
=
0
.
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Q1
If h, C and V respectively are the height, the curved surface and volume of cone, then
3
π
V
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−
C
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h
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+
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