A circus tent of height 15 m is in the form of cylinder of diameter 32 m and height 3m,
surmounted by a cone of the same radius. Find the volume of the tent and the cost of
the canvas at the rate of 110 per square metre.
curmounted by a
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9th
Maths
Surface Areas and Volumes
Surface Area of Right Circular Cylinders and Cones
A circus tent is in the for...
MATHS
A circus tent is in the form of a cone over a cylinder. The diameter of the base is 9 m, the height of cylindrical part is 4.8 m and the total height of the tent is 10.8 m. The canvas required for the tent is ..........
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ANSWER
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
=
2
9
m
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
=
2
9
m
Height of the conical part =10.8−4.8=6 m
For a cone, l=
h
2
+r
2
, where h is the height.
Hence, l=
6
2
+4.5
2
∴l=7.5 m
Hence, area of canvas =2×π×4.5×4.8+π×4.5×7.5
=76.95π
=241.84m
2