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Q.

A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m   and 4 m   respectively and the slant height of the top is 2.8 m  , then what is the area of the canvas used for making the tent and also the cost of the canvas of the tent at the rate of Rs.500 per m 2  .


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a

Rs. 32000  

b

Rs. 24000  

c

Rs. 22000  

d

Rs. 20000   

answer is C.

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Detailed Solution

Given that the height and diameter of the cylindrical part are 2.1m and 4m, the slant height of the top is 2.8 m  and the rate is Rs.500 per m 2  .
We have the following formulae,
Curved area of conical part = πrl  
Curved area of cylindrical part = 2πrh  
Then for cone,
r = 2m
l = 2.8m
Cylinder,
r = 2m
h = 2.1m
Area canvas used will be,
Curved Area of conical part + Curved Area of cylindrical part
=π×2×2.8+2π×2×2.1 =2π[2.8+4.2] =2× 22 7 ×7 =44 m 2  
Cost of 1  m 2  canvas is Rs.500
Cost of 44  m 2   canvas is,
44×500 =Rs.22000  
Thus, the cost is Rs. 22000  .
Therefore the correct option is 3.
 
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