twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S' find the (a) radius r' of the new sphere (b) ratio of S and S'
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>>Volume of a Sphere
>>Twenty seven solid iron spheres, each of
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Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S
′
. Find the
(i) radius r
′
of the new sphere and
(ii) ratio of S and S
′
Medium
Solution
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(i) Radius of 1 solid iron sphere =r
⇒Volume =
3
4
πr
3
⇒Volume of 27 solid iron spheres =27×
3
4
πr
3
⇒
3
4
πr
′
3
=27×
3
4
πr
3
r
′
3
=2πr
3
⇒r
′
=3r
(ii) Surface area =4πr
2
SA r
′
=4πr
′
2
=4π(3r)
2
=36πr
2
S
′
S
=
36πr
2
4πr
2
=
9
1
=1:
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