| The length of canvas 75 cm wide required to build a conical tent of height 14 m and the floor are \[346.5\,\,{{m}^{2}},\]is [SSC (CGL) 2015] |
A) \[665\,\,m\]
B) \[770\,\,m\]
C) \[490\,\,m\]
D) \[860\,\,m\]
Correct Answer: B
Solution :
| Given, floor area \[=346.5\,\,{{m}^{2}}\] |
| \[\therefore \] \[\pi {{r}^{2}}=346.5\]\[\Rightarrow \]\[{{r}^{2}}=\frac{346.5}{22}\times 7\] |
| \[\Rightarrow \] \[{{r}^{2}}=110.25\]\[\Rightarrow \]\[r=10.5\,\,m\] |
| \[\Rightarrow \] \[l=\sqrt{{{r}^{2}}+{{h}^{2}}}=\sqrt{{{(10.5)}^{2}}+{{(14)}^{2}}}\] |
| \[=\sqrt{110.25+196}=\sqrt{306.25}=17.5\,\,m\] |
| \[\therefore \]Area of canvas = Area of cone |
| \[\Rightarrow \]\[l\times b=\pi rl\]\[\Rightarrow \]\[l\times \frac{75}{100}=\frac{22}{7}\times 10.5\times 17.5\] |
| \[\Rightarrow \]\[l=\frac{22\times 10.5}{7\times 75}\times 17.5\times 100\]\[\Rightarrow \]\[l=770\] |
| \[\therefore \]Length of canvas \[=770\,\,m\] |
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