| The length of canvas 75 cm wide required to build a conical tent of height 14 m and the floor area \[346.5\,{{m}^{2}},\] is |
| [SSC (CGL) Pre 2015] |
A) 665 m
B) 770 m
C) 490 m
D) 860 m
Correct Answer: B
Solution :
| Given, floor area \[346.5{{m}^{2}}\] |
| \[\therefore \] \[\pi {{r}^{2}}=346.5\]\[\Rightarrow \]\[{{r}^{2}}=\frac{346.5}{22}\times 7\] |
| \[\Rightarrow \] \[{{r}^{2}}=11025\]\[\Rightarrow \]\[r=10.5\,m\] |
| Now, \[l=\sqrt{{{r}^{2}}+{{h}^{2}}}=\sqrt{{{(10.5)}^{2}}+{{(14)}^{2}}}\] |
| \[=\sqrt{110.25+196}=\sqrt{306.25}=17.5\,m\] |
| \[\therefore \] Area of canvas = Area of cone |
| \[\Rightarrow \] \[l\times b=\pi rl\] |
| \[\Rightarrow \] \[l\times \frac{75}{100}=\frac{22}{7}\times 10.5\times 17.5\] |
| \[\Rightarrow \] \[l=\frac{22\times 10.5}{7\times 75}\times 17.5\times 100\] |
| \[\therefore \] \[l=770\] |
| \[\therefore \] Length of canvas = 770 m |
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