the diameter of cross section of a wire is reduced by 50% . if the volume remains constant , what percent of length of wire should be increased.
Answers
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Explanation:
Let r be the radius of cross-section of wire and h be its length.
Then volume =πr
2
h....(i)
5% of diameter of cross-seciton =
100
5
×2r=
10
r
New diameter =2r−
10
r
=
10
19r
New radius =
20
19r
Let new length be h
1
.
Volume =π(
20
19r
)
2
h
1
...(ii)
From (i) and (ii) we have
πr
2
h=(
20
19r
)
2
h
1
⇒h=
400
361
h
1
⇒h
1
=
361
400
h
Increase in length =h
1
−h=
361
400
−h=
361
39h
Percentage increase in length =
h
h
1
−h
×100=
h
39h
×100
=
361
3900
=10.8%
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