A) 11 cm
B) 12 cm
C) 14 cm
D) 16 cm
Correct Answer: C
Solution :
| Inner toner radius (r) \[=\frac{4}{2}=2\,\,\text{cm}\] |
| Outer radius (R)\[=\frac{8}{2}=4\,\,\text{cm}\] |
| Volume of metal of the sphere \[=\frac{4}{3}\pi {{R}^{3}}-\frac{4}{3}\pi {{r}^{3}}\] |
| \[=\frac{4}{3}\pi ({{4}^{3}}-{{2}^{3}})=\frac{4}{3}\pi \times 56\,\,\text{c}{{\text{m}}^{3}}\] |
| Radius of base of cone \[(x)=\frac{8}{2}=4\,\,\text{cm}\] |
| \[\therefore \]\[\frac{1}{3}\pi {{4}^{2}}h=\frac{4}{3}\pi 56\](by condition) |
| \[\therefore \] \[h=\frac{\frac{4}{3}\times 56\times 3}{16}=14\,\,\text{cm}\] |
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