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Question
The interior of a building is in the form of a cylinder of base radius 12 m and height 3.5 m, surmounted by a cone of equal base and slant height 12.5 m. Find the internal curved surface area and the capacity of the building.
Solution
Height of the cone
`=sqrt((12.5)^2 - (12)^2)`
`=sqrt(12.25)`
`= 3.5m`
Capacity (volume) of cone
`=1/3 pir^2h`
`=1/3 xx 22/7 xx 12 xx 3.5`
`=528 m^3`
Capacity (volume) of cylinder
`=pir^2 h`
`=22/7 xx 12xx 12 xx 3.5`
`=1584 m^3`
Therefore,
Total capacity of building
`= 1584 + 528`
`=2112 m^3`
Internal curved surface area of the building
`=2pirh + pirl`
`= pir(2h+l)`
`=22/7 xx 12 (2 xx 3.5 + 12.5)`
`=22/7 xx 12 xx 19.5`
`=735.43m^2`
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