A) \[\frac{3R_{1}^{2}-30}{7{{R}_{1}}}\]
B) \[\frac{R_{1}^{2}-40}{R_{1}^{2}}\]
C) \[\frac{30-{{R}_{1}}}{R_{1}^{2}}\]
D) \[\frac{40-R_{1}^{2}}{{{R}_{1}}}\]
Correct Answer: D
Solution :
| [d] According to the question, Area of circular shell = Total surface area of cylinder \[\Rightarrow \] \[\pi \,({{12}^{2}}-{{8}^{2}})=2\pi \,{{R}_{1}}({{R}_{1}}+h)\,\] \[\Rightarrow \] \[80\pi =2\pi \,(R_{1}^{2}+{{R}_{1}}h)\] \[\Rightarrow \] \[40=R_{1}^{2}+{{R}_{1}}h\] \[\Rightarrow \] \[{{R}_{1}}h=40-R_{1}^{2}\] \[\therefore \] \[h=\frac{40-R_{1}^{2}}{{{R}_{1}}}\] |
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