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.

Answer 1

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`