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Byju's Answer
Standard IX
Mathematics
Volume of a right circular cone
If h , C , V ...
Question
If h, C, V are respectively the height, the curved surface and volume of a cone, prove that
3
π
V
h
3
−
C
2
h
2
+
9
V
2
=
0
. [4 MARKS]
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Solution
Concept: 1 Mark
Formula: 0.5 Mark each
Application: 1.5 Marks
Let
r
and
l
denote respectively the radius of the base and slant height of the cone.
l
2
=
r
2
+
h
2
,
V
=
1
3
π
r
2
h
,
C
=
π
r
l
3
π
V
h
3
−
C
2
h
2
+
9
V
2
=
3
π
×
1
3
π
r
2
h
×
h
3
−
(
π
r
l
)
2
h
2
+
9
×
(
1
3
π
r
2
h
)
2
=
π
2
r
2
h
4
−
π
2
r
2
l
2
h
2
+
π
2
r
4
h
2
=
π
2
r
2
h
4
−
π
2
r
2
(
r
2
+
h
2
)
h
2
+
π
2
r
4
h
2
=
π
2
r
2
h
4
−
π
2
r
4
h
2
−
π
2
r
2
h
4
+
π
2
r
4
h
2
=
0
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