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UPSC CDS Math Volume and Surface Area Questions
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© examsnet.com
Question : 13
Total: 104
The volume of a spherical balloon is increased by 700%. What is the percentage increase in its surface area ?
[2019 CDS-I]
300%
400%
450%
500%
Validate
Solution:
New volume of balloon = V + 700% of V = 8V
Let r be the initial radius and R be the new radius of the balloon.
R
3
r
3
=
8
V
V
=
8
⇒
R
r
=
2
⇒
R
=
2
r
Initial surface area of balloon
=
4
π
r
2
New surface area of balloon
=
4
π
(
2
r
)
2
=
16
π
r
2
Percentage increase in surface area
=
(
16
π
r
2
−
4
π
r
2
)
4
π
r
2
×
100
=
300
%
© examsnet.com
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