A tent is in the form of a cylinder of diameter 4.2 m and height 8 m surmounted
by a
cone of equal base and height 6 m. Find the volume of the air in the tent.
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The amount of canvas used to make the tent = Curved surface area of cylindrical part + Curved surface area of the conical part.
Curved Surface Area of a Cylinder of Radius R and height h
=2πRh
Radius of the cylindrical part =
2
Diameter
=4m
Curved surface area of a cone =πrl, where r is the radius of the cone and l is the slant height.
Radius of the conical part =
2
Diameter
=4m
For a cone, l=
h
2
+r
2
, where h is the height
=
3
2
+4
2
l=5m
Hence, area of canvas =(2×π×4×2)+(π×4×5)=36πm
2
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