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Q.

What will be the area of canvas needed to make the tent, if a circus tent is cylindrical to a height of 3 m and conical above it, with its base radius as 52.5 m and the slant height of the conical portion as 53 m?

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a

9735  m 2  

b

9745  m 2  

c

9750  m 2   

d

9740  m 2  

answer is A.

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Detailed Solution

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A circus tent is cylindrical up to a height of 3m and conical above. If the  diameter of the base is 105m and the slant height of the conical part is 53m  ,

Cylinder: 

Radius of the cylinder, R=52.5 m

Height of the cylinder, H= 3 m

Cone: 

Radius of the cylinder, r=52.5 m

Slant height, l= 53 m

We know that, curved surface area of the cylinder = 2πrh

And the curved surface area of the cone = πrl 

The area of canvas needed to make the tent 

= Surface area of the tent 

= Curved surface area of the cylindrical portion + curved surface area of conical portion 

2πRH+πrl 

2×227×52.5×3+227×52.5×53

990+8745 

9735 

Hence, the total area of canvas required for making the tent is 9735  m 2 .

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