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Byju's Answer
Standard X
Mathematics
Volume of a Sphere
The diameter ...
Question
The diameter of a right circular cylinder is decreased by 10%. The volume of cylinder remains the same , then the percentage increase in height is _
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Solution
Dear Student,
Let
h
be
the
initial
height
and
r
=
d
2
be
the
initial
radius
and
H
,
R
,
D
be
the
height
,
radius
and
diameter
after
changing
the
diameter
Initial
Volume
=
v
=
πr
2
h
As
diameter
is
decreased
by
10
%
⇒
10
%
of
d
=
10
100
×
d
=
d
10
D
=
d
-
d
10
=
9
d
10
R
=
D
2
=
9
d
10
×
2
=
9
r
10
Volume
after
change
=
V
=
πR
2
H
as
V
=
v
⇒
πr
2
h
=
πR
2
H
⇒
πr
2
h
=
π
(
9
r
10
)
2
H
⇒
h
=
81
100
H
⇒
H
=
100
h
81
Now
,
increase
in
height
=
H
-
h
=
100
h
81
-
h
=
19
h
81
Percent
increase
in
height
=
19
h
81
h
×
100
%
=
23
.
45
%
Regards
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