Shantanu's cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 5 such caps. |
A) \[5000\,\,c{{m}^{2}}\]
B) \[2750\,\,c{{m}^{2}}\]
C) \[3000\,\,c{{m}^{2}}\]
D) \[2700\,\,c{{m}^{2}}\]
E) None of these
Correct Answer: B
Solution :
Here, \[r=7\,\,cm\] and \[h=24\,\,cm\] |
Slant height \[(l)=\sqrt{{{r}^{2}}+{{h}^{2}}}\] |
\[=\sqrt{{{7}^{2}}+{{24}^{2}}}\] |
\[=\sqrt{49+576}\] |
\[=\sqrt{625}=25\,\,cm\] |
Curved surface area \[=\pi rl\] |
\[=\frac{22}{7}\times 7\times 25=550\,\,c{{m}^{2}}\] |
\[\therefore \]Area of 5 caps \[=550\times 5\] |
\[=2750\,\,c{{m}^{2}}\] |
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