question_answer

A tent is in the shape of a right circular cylinder up to a height of 3 m and then becomes a right circular cone with a maximum height of 13.5 m above the ground. Calculate the cost of painting the inner side of the tent at the rate of \[Rs.\text{ }2\text{ }per\text{ }{{m}^{2}},\]if the radius of the base is 14 m.    

A)  Rs.2068                     

B)  Rs.2156                     

C)  Rs.2248                     

D)  Rs.1872                                 

Correct Answer: A

Solution :

Radius of cylinder = Radius of cone = 14 m. Height of cylinder \[=3\text{ }m~\] Height of cone \[=10.5\text{ }m\] Slant height of cone       \[=\sqrt{{{(10.5)}^{2}}+{{(14)}^{2}}}\] \[=17.5\,m\]       Total curved surface area of tent = Curved surface area of cylinder + Curved surface            area of cone \[=\pi (2\times 14\times 3+14\times 17.5)\] \[=\frac{22}{7}\times (84+245)=\frac{22}{7}\times 329=1034c{{m}^{2}}\] Cost of painting the inner surface at the rate of Rs. 2 per\[~{{m}^{2}}=2\times 1034=Rs.2068\]