A) 4 cm
B) 6 cm
C) 8 cm
D) 12 cm
Correct Answer: D
Solution :
According to the question, three metallic spheres are melted arid recast into a new solid sphered means that the volume of new solid sphere will be equal t& the sum of volumes of three solid sphere. \[\therefore \]Volume of new solid sphere \[=\frac{4}{3}\pi {{\left( \frac{6}{2} \right)}^{3}}+\frac{4}{3}\pi {{\left( \frac{8}{2} \right)}^{3}}+\frac{4}{3}\pi {{\left( \frac{10}{2} \right)}^{3}}\] \[\Rightarrow \] \[\frac{4}{3}\pi {{r}^{3}}=\frac{4}{3}\pi [{{(3)}^{3}}+{{(4)}^{3}}+{{(5)}^{3}}]\] \[\Rightarrow \] \[{{r}^{3}}=27+64+125\] \[\Rightarrow \] \[{{r}^{3}}=216\Rightarrow {{r}^{3}}={{(6)}^{3}}\]\[\Rightarrow \]\[r=6\,\,cm\] \[\therefore \]Diameter of the new sphere \[=2\times 6=12\,\,cm\]
You need to login to perform this action.
You will be redirected in
3 sec
