A) 12 cm
B) 7 cm
C) 14 cm
D) None of these
Correct Answer: C
Solution :
Internal volume of shell \[=\frac{4}{3}\pi {{(3)}^{3}}c{{m}^{3}}\] External volume of shell \[=\frac{4}{3}\pi {{(5)}^{3}}c{{m}^{3}}\] \[\therefore \] Volume of metal \[=\frac{4}{3}\pi {{(5)}^{3}}-\frac{4}{3}\pi {{(3)}^{3}}\] \[=\frac{4}{3}\pi (125-27)\] \[=\frac{4}{3}\pi \times 98\] Length of cylinder \[=\frac{8}{3}\,cm\] \[\therefore \] Volume of cylinder formed \[=\frac{4}{3}\pi \times 98\] \[\Rightarrow \] \[\pi {{r}^{2}}h=\frac{4}{3}\pi \times 98\] \[\Rightarrow \] \[{{r}^{2}}=\frac{4}{3}\times 98\times \frac{3}{8}\] \[\Rightarrow \] \[{{r}^{2}}=49\] \[\therefore \] \[r=7cm\] Here, diameter of cylinder \[=2\times 7=14\text{ }cm\]
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