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Byju's Answer
Standard IX
Mathematics
Volume of a cube
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Question
Find the approximate change in the volume
V
of a cube of side
x
meters caused by increasing the side by
2
%
.
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Solution
Given that the side of a cube is
x
meters
So, the volume of a cube will be
V
=
x
3
Now the side
x
is increased by
2
%
, so the new length of side will be
x
(
1
+
2
100
)
=
51
x
50
The new volume will be
V
1
=
(
51
x
50
)
3
=
(
51
50
)
3
x
3
Therefore, the change in volume is
V
1
−
V
=
(
(
51
50
)
3
−
1
)
x
3
The percentage change in volume is :
=
V
1
−
V
V
×
100
=
⎛
⎜ ⎜ ⎜ ⎜
⎝
⎛
⎝
51
50
⎞
⎠
3
−
1
1
⎞
⎟ ⎟ ⎟ ⎟
⎠
×
100
=
(
51
3
−
50
3
50
3
)
×
100
=
7651
125000
×
100
=
6.12
%
.
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Volume of a cube
Standard IX Mathematics
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