| The volume of a conical tent is 1232 cm am the area of its bases is \[14\,{{m}^{2}}.\] Find the length of the canvas required to build the tent, if the canvas is 2 m in width. \[\left( take\,\pi \frac{22}{7} \right)\] |
A) 270 m
B) 272 m
C) 276 m
D) 275 m
Correct Answer: D
Solution :
| Let radius of base of conical tent be r cm and its height be hem. |
| Then |
| \[\pi {{r}^{2}}=154\]\[\Rightarrow \]\[{{r}^{2}}=154\times \frac{7}{22}=49\]\[\Rightarrow \]\[r=7\,cm\] |
| and \[\frac{1}{3}\pi {{r}^{2}}h=1232\] |
| \[\Rightarrow \] \[h=1232\times 3\times \frac{7}{22}\times \frac{1}{7\times 7}=24\,cm\] |
| Now, \[l=\sqrt{{{r}^{2}}+{{h}^{2}}}=\sqrt{49+576}=\sqrt{625}=25\,cm\] |
| \[\therefore \] Area of required canvas |
| = Curved surface of tent \[=\pi rl\] |
| \[=\frac{22}{7}\times 7\times 25=550\,c{{m}^{2}}\] |
| \[\therefore \] Length of canvas \[=\frac{550}{2}=275\,m\] |
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