A military tent is made as a combination of right circular cylinder and right circular cone on top.
Given :
Total Height of tent = h = 8.25 m
Base diameter of tent = 30 m, then
Base radius of tent = r = 30/2 m = 15 m
Height of right circular cylinder = 5.5 m
Base radius of cone = 15 m
Let slant height of cone = l m
Now,
Curved surface area of right circular cylindrical part of tent = 2πrh
and
Height of conical part = total height of tent – height of cylindrical part
Height of cone = 8.25 – 5.5 = 2.75 m
l2 = h2 + r2
= 2.752 + 152
= 232.5625
or l = 15.25 m
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
= 1237.5
Total surface area of tent is 1237.5 m2
Breadth of canvas used = 1.5 m
Length of canvas used x breadth of canvas used = Total surface area of tent
Length of canvas used = 1237.5\1.5 = 825
Length of canvas used is 825 m. Answer!!