question_answer

If a right circular cone of height 24 cm has a volume of \[1232\,\,c{{m}^{2}},\] then the area of its curved surface \[(Take\,\,\pi =\frac{22}{7})\] is

A)  \[1254\,\,c{{m}^{2}}\]           

B)  \[704\,\,c{{m}^{2}}\]

C)  \[550\,\,c{{m}^{2}}\] 

D)  \[157\,\,c{{m}^{2}}\]

Correct Answer: C

Solution :

Volume of the cone \[=\frac{1}{3}\pi {{r}^{2}}h\] \[\Rightarrow \]   \[1232=\frac{1}{3}\times \frac{22}{7}\times {{r}^{2}}\times 24\] \[\Rightarrow \]   \[{{r}^{2}}=\frac{1232\times 3\times 7}{22\times 24}=49\] \[\therefore \]      \[r=7\]   \[\therefore \] Slant height \[=\sqrt{{{(24)}^{2}}+{{(7)}^{2}}}\]                         \[=\sqrt{576+49}=\sqrt{625}=25\,\,cm\] Area of curved surface \[=\pi rl\]             \[=\frac{22}{7}\times 7\times 25=550\,\,c{{m}^{2}}\]