| A metallic sphere of radius 12 cm is melted into three smaller spheres. If the radii of two smaller spheres are 6 cm and 8 cm, the radius of the third is |
A) 14 cm
B) 16 cm
C) 10 cm
D) 12 cm
Correct Answer: C
Solution :
| Let radius of the third sphere be r cm. |
| Then, \[\frac{4}{3}\pi \times \,\,{{(12)}^{3}}=\frac{4}{3}\pi \times {{(6)}^{3}}+\frac{4}{3}\pi \times {{(8)}^{3}}+\frac{4}{3}\pi {{r}^{3}}\] |
| \[\Rightarrow \] \[{{(12)}^{3}}={{(6)}^{3}}+{{(8)}^{3}}+{{r}^{3}}\] |
| \[\Rightarrow \] \[{{r}^{3}}=1728-216-512\]\[\Rightarrow \]\[{{r}^{3}}=1000\] |
| \[\therefore \] \[r=10\,\,cm\] |
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