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 canvas used in making the tent, if the breadth of the canvas is 1.5 m.
Answers
Step-by-step explanation:
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=
(r
2
+h
2
)
where, r= radius of base and h= altitude height of cone
radius of cylinder = radius of cone
therefore radius of cone=
2
30
=15 m
l=
(r
2
+h
2
)
l=
(15
2
+2.75
2
)
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 m
2
∴ Length of canvas =
1.5
1236.47
= 824.3