Question

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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Answer 1

Answer:

(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