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UPSC 2015 CDS II Math Paper
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© examsnet.com
Question : 62
Total: 100
From the solid gold in the form of a cube of side length 1 cm, spherical solid balls each having the surface area
π
1
3
c
m
2
are to be made. Assuming that there is no loss of the material in the process of making the balls, the maximum number of balls made will be
[2015 CDS-II]
3
4
6
9
Validate
Solution:
Let r be the radius of each spherical ball.
∴
4
π
r
=
π
1
3
⇒
r
2
=
1
4
π
2
3
⇒
r
=
1
2
π
1
3
c
m
Let the number of balls formed be n.
∴
n
=
Volume of the cube
Volume of each spherical ball
=
1
3
4
3
π
×
(
1
2
π
1
3
)
=
6
Thus, the maximum number of balls formed are 6
© examsnet.com
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