A military tent of height 8.25m is in the form of a right circular cylinder of base diameter 30 m and height 5.5 m surmounted by a right circular cone of a same base radius. Find the length of canvas used in making the tent, if the breadth of the canvas is 1.5 m.

The military tent is made as a combination of right circular cylinder and right circular cone on top.


Total Height of tent = h = 8.25 m


Base diameter of tent = 30 m


Base radius of tent = r = 30/2 m = 15 m


Height of right circular cylinder = 5.5 m


Curved surface area of right circular cylindrical part of tent = 2πrh


Height of conical part = total height of tent – height of cylindrical part


hcone = 8.25 – 5.5 m = 2.75 m


Base radius of cone = 15 m


Let l be the slant height of cone


Then, l2 = hcone2 + r2 = 2.752 + 152 m2


l2 = 7.5625 + 225 m2 = 232.5625


l = 15.25


Curved surface area of conical part of the tent = πrl


Total surface area of the tent = Curved surface area of cylindrical part + curved surface area of conical part


Total surface area of tent = 2πrh + πrl


= πr (2h + l)


= 22/7 × 15 × (2 × 5.5 + 15.25) m2


= 22/7 × 15 × (11 + 15.25) m2


= 22/7 × 15 × 26.25 m2


= 1237.5 m2


Breadth of canvas used = 1.5 m


Length of canvas used = Total surface area of tent ÷ breadth of canvas used


Length of canvas used = 1237.51.5 m = 825 m


Length of canvas used is 825 m.


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