A military tent of height 8.25m is in the form of a right circular cylinder of base diameter 30m and height 5.5m surmounted by a right circular cone of same base radius. Find the length of the canvas use in making the tent, if the breadth of the canvas is 1.5m.
Height of the military tent = Height of the circular cylinder + Height of the right circular cone
Given,
Height of the military tent = 8.25m
Height of the circular cylinder =5.5m
Height of the right circular cone =8.25−5.5
therefore Height of the right circular cone = 2.75m
We know that,
The slant height of a cone, l=√(r2+h2)
where, r= radius of base and h= altitude height of cone
radius of cylinder = radius of cone
therefore radius of cone=302=15 m
l=√(r2+h2)
l=√(152+2.752)
l=√(225+7.5625)
slant height, l=15.25 m
Surface area of cone =π r l =π×15×15.25= 718.9 m
Surface area of cylinder =2 π r h =2×π×15×5.5= 518.57 m
Area of the canvas = Surface area of cone + Surface area of cylinder
=718.9+518.57
=1236.47 m2
∴ Length of canvas = 1236.471.5 = 824.3 m