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,
ii)ratio of S and S'.
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(i) Radius of 1 solid iron sphere =r
⇒Volume =34πr3
⇒Volume of 27 solid iron spheres =27×34πr3
⇒34πr′3=27×34πr3
r′3=2πr3
⇒r′=3r
(ii) Surface area =4πr2
SA r′=4πr′2
=4π(3r)2=36πr2
S′S=36πr24πr2=91=1:9
supriyaverma80:
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