A) 4 : 1
B) 1 :16
C) 16 : 1
D) 1 : 4
Correct Answer: C
Solution :
Volume of the solid metallic Sphere \[=\frac{4}{3}\pi {{r}^{3}}=\frac{4}{3}\times \pi \times {{(8)}^{3}}=\frac{2048}{8}\pi \,\,c{{m}^{3}}\] Let the radius of the each small sphere = x cm \[\therefore \] \[64\times \frac{4}{3}\pi {{x}^{3}}=\frac{2048}{3}\pi \] \[\Rightarrow \] \[{{x}^{3}}=\frac{2048}{64\times 4}=8\] \[\Rightarrow \] \[x=\sqrt[3]{8}=2\,\,cm\] \[\Rightarrow \] Required ratio \[=4\pi {{(8)}^{2}}:4\pi {{(2)}^{2}}=64:4=16:1\]
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