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Standard IX
Mathematics
Volume of a sphere
A cylinder, a...
Question
A cylinder, a hemisphere, and a cone have an equal base diameter and have the same height. Prove that their volume are in the ratio
3
:
2
:
1
.
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Solution
For cylinder,
R
a
d
i
u
s
=
H
e
i
g
h
t
=
r
For hemisphere,
R
a
d
i
u
s
=
r
For cone,
R
a
d
i
u
s
=
H
e
i
g
h
t
=
r
Volume of cylinder =
π
r
2
h
=
π
r
3
Volume of hemisphere =
2
3
π
r
3
Volume of Cone =
1
3
π
r
2
h
=
1
3
π
r
3
Hence, ratio of Volumes is:
1
:
2
3
:
1
3
=
3
:
2
:
1
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