question_answer

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 \[=550\times 5\]

\[=2750\,\,c{{m}^{2}}\]