If the radius and height of a cone are increased by 5%, then find the the increase in volume of the cone ?
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1
Answer:
Let initial radius of cone =r
1
and initial height of cone =h
1
.
Initial volume of cone, V
1
=
3
1
πr
1
2
h
1
.
After increasing, radius of cone =r
2
and height of cone =h
2
.
Then, r
2
=r
1
+
100
10
r
1
=
10
11
r
1
and h
2
=h
1
+
100
10
h
1
=
10
11
h
1
.
Therefore, New volume, V
2
=
3
1
πr
2
2
h
2
=
3
1
π×(
10
11
)
2
r
1
2
×(
10
11
)
2
h
1
⟹ V
2
=
3
1
πr
1
h
1
×
1000
1331
⟹ V
2
=
1000
1331
V
1
.
Percentage increase in volume =
V
1
V
2
−V
1
×100%
=
V
1
1000
1331V
1
−V
1
×100=
1000V
1
331V
1
×100=33.1%.
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