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CBSE Class 9 Answered

A building is cylindrical to a height of 9 m and conical above it. If the base radius is 15 m and height of the cone is 8 m, find the area of the building.
Asked by Topperlearning User | 17 Oct, 2017, 09:06: AM
answered-by-expert Expert Answer

Diameter= 24 m

⇒ radius =12 m

Radius of the conical part = Radius of the cylindrical part (r) = 15 m

Height of cylindrical part (h) = 9 m, height of the cone (h) = 8 m

For the conical part of the building,

begin mathsize 12px style l squared space equals space straight r squared space plus space straight h squared l italic space italic space italic space equals space square root of space straight r squared space plus space straight h squared end root l italic space italic space space equals italic space square root of 15 squared space plus space 8 squared end root italic space l italic space italic space equals 17 space straight m end style

Thus, l = 17 m

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

 

begin mathsize 12px style equals space πr l italic space plus space 2 πrh equals space πr space left parenthesis l italic space plus space 2 straight h right parenthesis equals space 22 over 7 cross times 15 cross times open parentheses 17 space plus space 18 close parentheses equals space 22 over 7 cross times 15 divided by 35 equals space 1650 space straight m squared end style

The surface of the building is 1650 m2

Answered by | 17 Oct, 2017, 11:06: AM

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