A) 270 m
B) 272 m
C) 276 m
D) 275 m
Correct Answer: D
Solution :
[d] Let radius of base of conical tent be r m and it's height be h m. Then,\[\pi {{r}^{2}}=154\] \[\Rightarrow \] \[{{r}^{2}}=154\times \frac{7}{22}=49\] \[\Rightarrow \] \[r=7\,m\]and \[\frac{1}{3}\pi {{r}^{2}}h=1232\] \[\Rightarrow \] \[h=1232\times 3\frac{7}{22}\times \frac{1}{7\times 7}=24\,m\] Now, \[l=\sqrt{{{r}^{2}}+{{h}^{2}}}\] \[=\sqrt{49+576}=\sqrt{625}=25\,m\] \[\therefore \]Area of required canvas = Curved surface of tent \[=\pi rl=\frac{22}{7}\times 7\times 25\] \[=550\,sq\,cm\] \[\therefore \]Length of canvas \[=\frac{550}{2}=275\,m\] |
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