A circus tent is cylindrical up to a height of 3.3 m and conical above it .if the diameter of the base is 100m and slant height of the conical part is 56.4 ,find the total canvas used in making the tent . if the cost of canvas is RS 8 m square ,find the total cost of canvas required in making the tent.
Answers
Step-by-step explanation:
Total cost of canvas required in making the tent is 204728 Rs
Step-by-step explanation:-
Given:-
(i) Height of the cylindrical tent(h) = 3.3m
(ii) Diameter of it's base = 100m
(iii) Radius(r) = 100/2 = 50m
Therefore:-
Formula for the total surface area of the cylindrical tent = 2πr(r+h)
=> 2 x 3.14 x 50(50 + 3.3)
=> 6.28 x 50(53.3)
=> 6.28 x 2665
=> 16,736.2m²
Now:-
In case of the conical part above the cylinder,
We Have:-
(i) Slant height of the cone (l) = 56.4m and
(ii) Radius (r) = 50m
As we know that the curved surface area of the cone = πrh
On putting the values:-
=> 3.14 x 50 x 56.4
=> 157 x 56.4
=> 8854.8m²
Now the total surface area of both the the cone and cylinder will be
=> C.S.A. of Cone + T.S.A. of tent
=> 8854.8m² + 17,736.2m²
=> 25,591m².
Finally it is given that the cost of 1m² canvas is 38 rupees
Therefore:-
Cost of 25,591m² canvas = Cost x Area
=>8*25591
= 204728.
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