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CBSE Class 9 Answered

A circus tent is cylindrical upto a height of 11 m and conical above it. If the diameter of the base is 24 m and the height of the cone is 5 m, find the length of the canvas required to make the tent if the width of the canvas is 5 m.
Asked by Topperlearning User | 17 Oct, 2017, 08:59: AM
answered-by-expert Expert Answer

Diameter= 24 m radius =12 m

Radius of the conical part = Radius of the cylindrical part (r) = 12 m

Height of cylindrical part (h) = 11 m, height of the cone (h) = 5 m

For the conical part of the rocket,

  

begin mathsize 12px style l squared space equals space straight r squared space plus space straight h squared
l italic space equals space square root of space straight r squared space plus space straight h squared end root
l italic space italic equals italic space square root of italic 12 to the power of italic 2 italic plus italic 5 to the power of italic 2 end root
l italic space italic equals 13 space straight m
end style

Thus, l =13 m

Surface area of the tent = Curved surface area of the conical part + curved surface area of the cylindrical part

begin mathsize 12px style equals space πr l plus space 2 πrh
equals space πr space open parentheses l italic space plus space 2 straight h close parentheses
equals 22 over 7 cross times 12 open parentheses 13 space plus space 22 close parentheses
equals space 22 over 7 cross times 12 cross times 35
equals space 1320 space straight m squared end style

 Breadth of tarpaulin (B) = 5 m, let length of tarpaulin= L

Area of tarpaulin required = surface area of the tent

 

begin mathsize 12px style straight L cross times straight B space equals space 1320
straight L space equals space 1320 over 5 space
straight L space equals space 264 space straight m end style

Thus 264 m long tarpaulin is required.

 

Answered by | 17 Oct, 2017, 10:59: AM
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